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Annotation 1731573714188

#sprectral-theorem #stochastics

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In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem^[1]^[2] is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval.

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Karhunen–Loève theorem - Wikipedia
Karhunen–Loève theorem - Wikipedia Karhunen–Loève theorem From Wikipedia, the free encyclopedia (Redirected from Karhunen–Loeve expansion) Jump to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem [1] [2] is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. The transformation is also known as Hotelling Transform and Eigenvector Transform, and is closely related to Principal Component Analysis (PCA) technique widely used in image processing

Annotation 1732138896652

#spanish

Él seguía deprimido, aunque dijo que había dormido bien.

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Flashcard 1732485451020

Tags

#sprectral-theorem #stochastics

Question

the Karhunen–Loève theorem represents [...] as an infinite linear combination of orthogonal functions

Answer

a stochastic process

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d> Jump to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem [1] [2] is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. <html>

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Flashcard 1732487023884

Tags

#sprectral-theorem #stochastics

Question

the Karhunen–Loève theorem represents a stochastic process as [...]

Answer

an infinite linear combination of orthogonal functions

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p to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem [1] [2] is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. <body><html>

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Annotation 1738457615628

#spanish

Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, a pesar de que el delantero tiene solo seis meses restantes en su contrato.

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Mourinho: Alexis no llegó al Manchester United por dinero
Te gustan las de arriba. "Esas son muy agradables, tan naranjas, tan redondas, tan llenas de jugo, pero no puedes llegar allí, así que dices: 'No quiero ir allí' o 'No me gustaron, prefiero las otras'. ' Me recuerda esa historia ". Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, a pesar de que el delantero tiene solo seis meses restantes en su contrato. Al final, United no pagó una tarifa después de aceptar y permitir que Mkhitaryan se mude al Emirates. Sánchez ha firmado un contrato de cuatro años y medio en Old Trafford por valor de

Annotation 1738459712780

#spanish

Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura envidia.

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Mourinho: Alexis no llegó al Manchester United por dinero
ciones. Decidió venir aquí y tienes que preguntarle por qué". Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes. Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura envidia. Agregó: "Creo que Alexis me recuerda un poco de la historia, no sé, no es una historia, casi una metáfora, cuando ves el árbol con naranjas increíbles en la parte superior del árbo

Annotation 1738461285644

#spanish

Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes.

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Mourinho: Alexis no llegó al Manchester United por dinero
ó más dinero que nosotros, creo que incluso Everton gastó más dinero que nosotros. No creo que ese sea el problema. "No sé. Alexis podía ir a todas partes. Tenía muchas opciones. Decidió venir aquí y tienes que preguntarle por qué". Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes. Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratar

Annotation 1738462858508

#spanish

Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos.

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Mourinho: Alexis no llegó al Manchester United por dinero
el Manchester United sobre Manchester City no estuvo motivada por el dinero. United y City se enfrentaron cara a cara por el chileno este mes con el delantero moviéndose a Old Trafford y Henrikh Mkhitaryan firmando por el Arsenal a cambio. Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos. Lleva ESPN a todos lados Si quieres recibir alertas del Futbol Europeo, descarga la App ahora. espn.com/app » Él dijo en una conferencia de prensa el jueves: "Sé que si otros club

Annotation 1738464431372

#spanish

Jose Mourinho: Alexis Sánchez no se mudó al Manchester United por dinero

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Mourinho: Alexis no llegó al Manchester United por dinero
stos colores" 5hESPN Digital La Copa del Rey se tiñe de azulgrana 5hJordi Blanco | ESPN Digital Jugadores que militan en Europa tienen pie y medio en el Mundial 5hIván Cañada América cierra pase de Romero a Independiente 6hRicardo Cariño Jose Mourinho: Alexis Sánchez no se mudó al Manchester United por dinero El jugador chileno firmó contrato con el Manchester United el lunes. Manchester United/Man Utd via Getty Images Facebook Twitter Facebook Messenger Correo-e Comentar 9:20 AM CT Rob Daw

Flashcard 1738467314956

Tags

#spanish

Question

Jose Mourinho: Alexis Sánchez no [...] al Manchester United por dinero

Answer

se mudó

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Jose Mourinho: Alexis Sánchez no se mudó al Manchester United por dinero

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Flashcard 1738468887820

Tags

#spanish

Question

Se informó que City [...] de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez.

Answer

se retiró

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Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos. </

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Flashcard 1738470460684

Tags

#spanish

Question

Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha [...] los reclamos.

Answer

desestimado

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Flashcard 1738472033548

Tags

#spanish

Question

Sánchez [...] su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes.

Answer

selló

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Sánchez selló su movimiento a Old Trafford el lunes y se espera que haga su debut con el United en el enfrentamiento de la FA Cup con Yeovil Town en Huish Park el viernes. <

Original toplevel document

Flashcard 1738473606412

Tags

#spanish

Question

Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho [...] que podría tratarse de pura envidia.

Answer

sugirió

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Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura envidia.

Original toplevel document

Flashcard 1738475179276

Tags

#spanish

Question

Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura [...].

Answer

envidia

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><head> Pep Guardiola dijo que el City había decidido no firmar al jugador de 29 años en un intento por mantenerse "estable con los salarios", pero Mourinho sugirió que podría tratarse de pura envidia. <html>

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Flashcard 1738476752140

Tags

#spanish

Question

Las fuentes le han dicho a ESPN FC que Arsenal [...] inicialmente en 49.5 millones de dólares por Sánchez

Answer

cotizaba

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Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, a pesar de que el delantero tiene solo seis meses restantes en su contrato

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Flashcard 1738479635724

Tags

#spanish

Question

Las fuentes le han dicho a ESPN FC que Arsenal cotizaba inicialmente en 49.5 millones de dólares (£ 35 millones) por Sánchez en el período de transferencias de enero, [...] que el delantero tiene solo seis meses restantes en su contrato.

Answer

a pesar de

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Flashcard 1738586590476

Tags

#measure-theory #stochastics

Question

Radon, Fréchet, and others generalized the new real analysis to [...of...on...]

Answer

integrals of real-valued functions on arbitrary spaces

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What Kolmogorov did was to say that the new real analysis that had started with the PhD thesis of Henri Lebesgue (1902) and had been rapidly generalized to integrals of real-valued functions on arbitrary spaces by Radon, Fr´echet, and others (called Lebesgue integration or abstract integration) should also be used in probability theory

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Annotation 1741788941580

#linear-algebra

In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R³) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane containing them.

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Cross product - Wikipedia
edia, the free encyclopedia Jump to: navigation, search This article is about the cross product of two vectors in three-dimensional Euclidean space. For other uses, see Cross product (disambiguation). In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with dot product (projection product). If two vectors have the same

Annotation 1743950581004

#state-space-models

Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields.

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Belief propagation - Wikipedia
st of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (April 2009) (Learn how and when to remove this template message) Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each unobserved node, conditional on any observed nodes. Belief propagation is commonly used in artificial intelligence and information theor

Flashcard 1743952678156

Tags

#state-space-models

Question

[...] is also known as sum-product message passing

Answer

Belief propagation

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Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. </sp

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Flashcard 1744130936076

Tags

#state-space-models

Question

Belief propagation is also known as [...]

Answer

sum-product message passing

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Flashcard 1744254930188

Tags

#linear-algebra

Question

the cross product is [...123...].

Answer

one binary operation on two vectors in three-dimensional space (R³)

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In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane

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Flashcard 1744257289484

Tags

#linear-algebra

Question

the cross product is occasionally called directed area product to emphasize [...]

Answer

the geometric significance

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Flashcard 1749112720652

Tags

#hilbert-space

Question

Hilbert spaces are [...]: there are enough limits in the space to allow the techniques of calculus to be used.

Answer

complete

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Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used.

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Hilbert space - Wikipedia
e state of a vibrating string can be modeled as a point in a Hilbert space. The decomposition of a vibrating string into its vibrations in distinct overtones is given by the projection of the point onto the coordinate axes in the space. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces. The earliest Hilbert spaces were studied from this point o

Flashcard 1753209769228

Tags

#vector-space

Question

a norm is a function that assigns a [...] to each vector in a vector space

Answer

nonnegative length or size

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a norm is a function that assigns a strictly positive length or size to each vector (bar zero vector) in a vector space

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Norm (mathematics) - Wikipedia
analysis. For field theory, see Field norm. For ideals, see Ideal norm. For group theory, see Norm (group). For norms in descriptive set theory, see prewellordering. In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).

Flashcard 1756885028108

Tags

#Karush-Kuhn-Tucker-condition #has-images

[unknown IMAGE 1756483423500]

Question

the function f(x) will only be at a maximum if λ satisfies [...formula...]

Answer

\( \lambda > 0 \)

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In optimization with inequality constraint, the sign of the Lagrange multiplier is crucial, because the function f(x) will only be at a maximum if its gradient is oriented away from the region g(x) > 0

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Annotation 1758542826764

[unknown IMAGE 1758545186060]

#has-images #sets

In mathematics, the infimum of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.

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Infimum and supremum - Wikipedia
ed sets the infimum and the minimum are equal. [imagelink] A set A of real numbers (blue balls), a set of upper bounds of A (red diamond and balls), and the smallest such upper bound, that is, the supremum of A (red diamond). In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists. Consequently, the term greatest lower bound (abbreviated as GLB) is also commonly used. The supremum (abbreviated sup; plural suprema) of a subset S of a partially ordered set T is th

Flashcard 1758547283212

Tags

#has-images #sets

[unknown IMAGE 1758545186060]

Question

the infimum of a subset S of a partially ordered set T is [...], if such an element exists.

Answer

the greatest element in T that is less than or equal to all elements of S

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In mathematics, the infimum of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.

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Flashcard 1758548856076

Tags

#has-images #sets

[unknown IMAGE 1758545186060]

Question

[...] is the greatest element in T that is less than or equal to all elements of S, if such an element exists.

Answer

the infimum of a subset S of a partially ordered set T

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In mathematics, the infimum of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.

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Flashcard 1759054269708

Tags

#linear-algebra

Question

the cross product is occasionally called [...] to emphasize the geometric significance

Answer

directed area product

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Flashcard 1759663230220

Tags

#lebesgue-space

Question

L^p spaces are function spaces defined using a natural generalization of [...]

Answer

the p-norm for finite-dimensional vector spaces.

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In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.

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Lp space - Wikipedia
Lp space - Wikipedia L p space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910). L p

Annotation 1760853101836

#calculus

Calculation of the total derivative of with respect to

assumes that the other arguments too depend on t.

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Total derivative - Wikipedia
effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). Calculation of the total derivative of f {\displaystyle f} with respect to t {\displaystyle t} does not assume that the other arguments are constant while t {\displaystyle t} varies; instead, it assumes that the other arguments too depend on t {\displaystyle t} . The total derivative includes these indirect dependencies to find the overall dependency of f {\displaystyle f} on t

Annotation 1760855198988

#calculus

The total derivative of a function of several variables, e.g.,

, , , with respect to an exogenous argument

, is the limiting ratio of the change in the function's value to the change in the exogenous argument's value, taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function.

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Total derivative - Wikipedia
integral Line integral Surface integral Volume integral Jacobian Hessian Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e In the mathematical field of differential calculus, a total derivative or full derivative of a function f {\displaystyle f} of several variables, e.g., t {\displaystyle t} , x {\displaystyle x} , y {\displaystyle y} , etc., with respect to an exogenous argument, e.g., t {\displaystyle t} , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). Calculation of the

Flashcard 1760858606860

Tags

#calculus

Question

The total derivative is the [...description...]

Answer

limiting ratio of ∆ƒ/∆t

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The total derivative of a function of several variables, e.g., , , , with respect to an exogenous argument , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value, taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function.

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Flashcard 1760860179724

Tags

#calculus

Question

The total derivative taking into account the exogenous argument's [...] to the function

Answer

direct and indirect effects

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a function of several variables, e.g., , , , with respect to an exogenous argument , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value, taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function. <body><html>

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Flashcard 1760861752588

Tags

#calculus

Question

The [...] of a function of several variables, e.g.,

, , , with respect to an exogenous argument

is defined as

Answer

total derivative

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Flashcard 1760864111884

Tags

#calculus

Question

Calculation of the total derivative of with respect to

assumes that [...].

Answer

the other arguments too depend on t

status	not learned	measured difficulty	37% [default]	last interval [days]
repetition number in this series	0	memorised on		scheduled repetition
scheduled repetition interval		last repetition or drill

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Calculation of the total derivative of with respect to assumes that the other arguments too depend on t.

Edited, memorised or added to reading queue

on 21-Apr-2018 (Sat)

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Original toplevel document

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