context_before stringlengths 0 199 | equation stringlengths 5 80 | context_after stringlengths 0 249 | spoken_English stringlengths 0 119 |
|---|---|---|---|
The vehicle models | $ F $ | are further described in section | F |
and noise vector | $ \boldsymbol { b } $ | are plotted in Figure 2b . Train/test misclassification error is the percentage of misclassified samples while empirical loss is given by | b |
be the thresholded sample covariance estimator with thresholding parameter | $ \widehat { \rho } _N $ | . Then , for any | hat rho sub N |
$ U $ | is a symmetry if it stabilizes the state whose coefficients are given by the tensor | U | |
eqnarray where | $ u $ | is a quadruplet of fields . This uses the definitions | u |
The Pantheon+ dataset has been utilized in recent analyses of the | $ H_0 $ | tension , such as R22 and | H sub zero. |
$ V $ | , that satisfies that Lie ( | V | |
Let | $ \Gamma^j= ( G_j , \sigma_j , \mu_j ) $ | be | Gamma to the power of j equals open parenthesis G sub j, sigma sub j, mu sub j close parenthesis. |
$ t_ { \rm df } $ | that appears as a formal segment of the | t sub d f | |
where the observed power-law radiation spectrum in the period of | $ t_ { \rm obs } \sim [ 0,5 ] $ | ~s is shown with a black solid . | t sub obs is approximately distributed between 0 and 5. |
& | $ 2 $ | & | two |
this advantage reduces with noise strength ; at noise strengths of | $ 0.01\ % $ | and below our circuits underperform previous work . Also , our color code circuits still do n't outperform the surface code . The final case that we benchmarked was to | 0.01 percent. |
where | $ s_N \sim N^ { -b } $ | is the selection strength of the advantageous allele with | s sub N is similar to N to the power of negative b. |
where | $ 0 < p < 1 $ | . For any | 0 is less than p which is less than 1. |
for different | $ d_0 $ | . | d sub zero. |
essential and | $ ( 1+O ( \eps ) ) $ | -quasifuchsian surfaces | One plus big O of epsilon. |
maps | $ [ 0,1 ] $ | to | the interval from zero to one, inclusive. |
$ i $ | in | i | |
we expect the number of nontrivial Wilson lines to scale with | $ N_f $ | for large | N sub f. |
and for all | $ t > 0 $ | . | t greater than zero |
in | $ v $ | as | v |
we recover the derivative for general | $ m $ | and | m |
Such a relationship exists between | $ u_a $ | and | u sub a. |
$ QR_i $ | or | QR sub i. | |
Suppose that | $ 1 < p < \infty $ | and let | 1 is less than p and p is less than infinity. |
If | $ \gamma_1 $ | is not the first right contour point of | Gamma one. |
$ Q ( t ) $ | represents the work needed to perform an instantaneous coupling and decoupling , i.e . the parameters | Q of t | |
& The binary value that is equal to 1 if service instance | $ i $ | is available at time | i |
be a pre-Dynkin-system on | $ \Omega $ | . Then there is a unique family of maximal algebras | Omega. |
If | $ G $ | is connected , then the dimension of | G |
evolutionary tracks do not even penetrate the | $ T_\mathrm { eff } $ | range of Y Oph , as it is also shown by other evolutionary computations | T sub e-f-f |
\\ Configuration | $ 4 $ | & | four |
-calculus is parametrized over a signature | $ \Sigma $ | and a monad | Sigma. |
Two graphs | $ \Gamma_1 $ | and | Gamma one. |
% For | $ \alpha > 0 , $ | The Levy measure for the TGFNBP is given by % | Alpha is greater than zero. |
The notation | $ H_ { k , n } $ | for Harary graphs , where | H sub k comma n |
of | $ \mathfrak { gl } _1 $ | , containing all the | gl one. |
to the interval | $ \varphi_\sigma \in ( 0 , \pi ] $ | . The phase variable | phi sub sigma belongs to the interval from 0 to pi, inclusive. |
which is clearly | $ T $ | -equivariant . By Lemma | T |
without taking the shortcut | $ \ { v_1 , v_k\ } $ | and without exploring the leaves . Moreover , by assuming that the repeating pattern of | v sub 1, v sub k |
$ j $ | in | j | |
vertex | $ v\in V ( T ) $ | such that | v belongs to V of T. |
is the curve that follows the straight path | $ \rho_0 $ | from | rho sub zero. |
The genus is increasing exponentially in | $ N $ | . | N |
are generated from the parameters of | $ x $ | , it is proved that for every | x |
since | $ S $ | contains | S |
& | $ 1.50232 $ | & | one point five zero two three. |
and | $ f\in C^n ( [ a , b ] ) $ | . Then the function | f belongs to C to the power of n, open interval from a to b. |
is the compact SVD of | $ Y $ | with singular values | Y |
when | $ \hbar $ | is made to converge towards | h-bar. |
Slightly altering | $ \theta $ | breaks mirror symmetry , lowering the symmetry from | Theta. |
Let | $ n , k\in\N $ | and | n, k belong to the set of natural numbers. |
& | $ \Delta $ | & | Delta. |
where | $ \sigma= ( x , v ) $ | represents both continuous and discrete spin variables and the self-interaction term is | sigma equals open parenthesis x comma v close parenthesis. |
two different values | $ m=1 $ | and | m equals one. |
& | $ F_ { 1,2 } $ | & | F sub one comma two. |
Assume that | $ A $ | is a multiple class and that | A |
$ M $ | = 17.13 ; SD = 3.84 ) . | M | |
for each | $ m\ge m_0 $ | and every nef Cartier divisor | m greater than or equal to m sub zero. |
for both | $ \rho_1 ' ( x ) $ | and | rho one prime of x. |
the compressor running state | $ m $ | was registered and expressed as a binary signal | m |
and | $ 2\ , m_ { \rm pole } ^ { \rm MNA } $ | . Because we can use only the first two terms for | Two times m sub pole superscript MNA. |
is the pseudo dimension of the function class | $ \Omega $ | . | Omega. |
in contrast to the Cl | $ 3p $ | orbitals in the case of | Three p. |
be | $ mm $ | -fields over | mm |
drawing | $ w_1 , \ldots , w_R \sim \mathcal { N } ( 0 , I_D ) $ | i.i.d . induces a function | w sub 1, ellipsis, w sub R, sim N open parenthesis 0, I sub D close parenthesis |
\\ \hline ST+PST & | $ - $ | 26 & 8 & | minus |
-ring of smooth functions on | $ M $ | is fully faithful , and preserves finite products and transverse pullbacks . | M |
we now start with | $ W ' $ | having only the single row | W prime. |
is an encoder and | $ g ( \cdot ) $ | is a decoder , then the loss function of DSC-Net can be expressed as : | g of dot. |
the | $ - $ | 1~ | minus |
-close to the zero section in the | $ C^k $ | -norm . Then for any sufficiently large number | C raised to the power of k. |
is transitive then | $ \mathcal { G } $ | is compact and | G |
for | $ n $ | large enough , and this upper bound is strictly less than | n |
$ ( K ) $ | results in enhanced | K | |
refers to | $ t \to \pm\infty $ | . Solitons behave like quasiparticles . However for KdV there are only overtaking collisions . Thus for | t goes to positive or negative infinity. |
We study several properties of such a | $ \zeta $ | -function , and verify an equivariant version of the Fried conjecture in some examples . Several factors motivate our work on this equivariant extension . | zeta. |
In the case of the matter density field smoothed on a single scale | $ R $ | , this driving parameter is the variance , which acts as a clock from initial to late times ( | R |
with probability | $ 1-C/c_n $ | . Also , we have | One minus C divided by C sub n. |
and | $ \alpha $ | are dimensionless parameters , | Alpha. |
d random variables independent of | $ x_1 , \dots , x_N $ | having the distribution | x sub 1, dot dot dot, x sub N |
The real coefficients | $ n_\alpha ( \disp_i ) $ | are associated with site | n sub alpha, open parenthesis, d i s p sub i, close parenthesis. |
agent | $ j $ | does not decide 1 by the fifth line of | j |
we fix a uniformizer | $ \unif $ | of | Uniform distribution. |
if | $ B ' $ | is not an end-block , then the vertex | B prime. |
- | $ R $ | & based on | R |
94 | $ \pm $ | 0.57 | Plus or minus. |
$ j , k=1,2 $ | . This completes the proof . % | j, k equals one, two. | |
Since | $ Q $ | is a multiple of 4 , this is equivalent to | Q |
the adaptation stepsize sequences | $ \nu $ | , and the adjacent state swapping rate | nu. |
56 | $ \pm0.51 $ | & 3.29 | plus or minus zero point five one. |
by replacing | $ \mathbf { s } _i $ | with | s sub i. |
the cofibrant replacement differential graded | $ \mathcal { D } _X $ | -algebra under | D sub X. |
is a smooth transformation from | $ [ 0,1 ] $ | to | the interval from zero to one, inclusive. |
for the set of open covers of | $ p $ | . In symbols : | p |
let | $ \varphi $ | be a scalar field . Working in polar coordinates , | phi. |
Note that | $ Z [ J , J ] = 1 $ | since in this case the forward and backward evolution exactly cancels out or , in other words , | Z, open square bracket, J, comma, J, close square bracket, equals 1. |
and | $ k_\text { min } \approx 10^6 $ | . For a fraction of points , rough estimates of uncertainties in determining the autocorrelation are shown with error bars . % The decay of the auto-correlation function is sub-exponential | k sub min approximately 10 to the power of 6. |
we go in this process until we are convinced the formula is indeed true ? The answer is that no amount of checking constitutes a proof for all values of | $ n $ | n | |
all hyperbolic once-punctured torus bundle over | $ \ { \mathbb\ S^1 $ | brace, blackboard bold S superscript 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.