# Relating CNNs with brain: Challenges and findings

Reem Abdel-Salam
Department of Computer engineering
Cairo University
<EMAIL_ADDRESS>

###### Abstract

Conventional neural network models (CNN), loosely inspired by the primate
visual system, have been shown to predict neural responses in the visual
cortex. However, the relationship between CNNs and the visual system is
incomplete due to many reasons. On one hand state of the art CNN architecture
is very complex, yet can be fooled by imperceptibly small, explicitly crafted
perturbations which makes it hard difficult to map layers of the network with
the visual system and to understand what they are doing. On the other hand, we
don’t know the exact mapping between feature space of the CNNs and the space
domain of the visual cortex, which makes it hard to accurately predict neural
responses. In this paper we review the challenges and the methods that have
been used to predict neural responses in the visual cortex and whole brain as
part of The Algonauts Project 2021 Challenge: “How the Human Brain Makes Sense
of a World in Motion". (Cichy et al., 2021).

_Keywords_ CNNs $\cdot$ LSTM $\cdot$ human neuroscience $\cdot$ machine
learning $\cdot$ Computational Neuroscience

##  1 Introduction

Building visual encoding models that accurately predict visual responses is a
major challenge for today’s vision-based brain-machine interface techniques.
This goal can be met by employing functional magnetic resonance imaging
(fMRI), which measures brain activity in human subjects who are passively
viewing images/videos (Kay, 2018). Visual encoding models, in particular, can
be built based on blood-oxygen-level-dependent (BOLD) signals to predict
neural responses to arbitrary stimuli and thus develop a better understanding
of visual information processing in the human brain. The visual processing in
the brain from external visual stimuli is usually non-linear. In order to
simulate non-linear mapping between input visual stimuli and brain activity,
visual encoding models are used. However, one significant obstacle in this
modeling and prediction process is the difficulty in developing an effective
non-linear feature space to study the non-linearity of neural responses
(Naselaris et al., 2011).
In early visual encoding models, feature space are mainly constructed using
hand-crafted features inspired by some visual representation mechanisms. Kay
et al. (2008) used the Gabor wavelet pyramid model as the nonlinear feature
extractor from the stimulus space to the feature space, and receptive-field
models to predict brain activity. The Gabor wavelet pyramid became a classical
encoding model for low-level visual information, especially when predicting
brain activity in the V1 region. Many following studies enhanced the Gabor
wavelet pyramid model’s fundamental characteristics and prediction outputs as
in (Huth et al., 2012; Stansbury et al., 2013). Nishimoto et al. (2011)
proposed using a fixed set of nonlinear spatiotemporal motion-energy filters
and then a set of hemodynamic response filters fit separately to each voxel.
Encoding models based on handcrafted features have high biological
interpretability but poor prediction performance and universality because they
are often created for a few specific visual regions.
Deep neural networks (DNNs) with hierarchical feature transformation have
recently made achievements in a range of disciplines (including computer
vision), capturing the attention of computational neuroscience researchers.
Numerous neuroscience methods have used convolutional neural networks (CNNs)
to represent the human visual system, achieving tremendous advancements in
building visual encoding models. In general, these CNN-based visual encoding
modeling approaches can be divided into task-driven and data-driven
approaches. In task-driven approaches usually, neural responses are generated
by using activation features in intermediate layers in pre-trained CNNs on a
vision task as imagenet. Agrawal et al. (2014) investigated two models Fisher
Vectors and Convnets to produce features in order to predict brain activity
across many low- and high-level visual areas. Güçlü and van Gerven (2015) used
two different CNNs for layer-wise analysis of voxel scores in the ventral
stream. Shi et al. (2018) proposed adding a recurrent neural network (RNN) to
a pre-trained CNN (VGG16) in order to predict cortical fMRI responses to
natural movie stimuli. The RNN better predicted cortical responses to natural
movie stimuli than the CNN, at all visual areas, especially those along the
dorsal stream. This demonstrates the potential of using the RNN for in-depth
computational understanding of the dynamic natural vision. Han et al. (2019)
proposed a variational auto-encoder (VAE), as a computational model of the
visual cortex. The first five layers of the VAE acts as an encoder while the
last five layers act as a decoder to learn visual representations from a
diverse set of unlabeled images. To elicit visual cortical responses, data-
driven techniques immediately train all parameters of a given encoding model
based on experimental inputs. Zhang et al. (2019) used transfer learning to
incorporate a previously trained DNN and build a nonlinear mapping from visual
features to brain activity. This nonlinear mapping replaces traditional linear
mapping and is intended to improve brain activity prediction accuracy. Qiao et
al. (2021) proposed an end-to-end CNN regression model for visual encoding
based on fMRI data. As a result, this model could develop appropriate feature
representations and linear regression weights for visual cortical responses
while also significantly improving prediction performance. Cui et al. (2021)
proposed GaborNet visual encoding an end to end encoding model, combining
handcrafted and deep ROI features. The key idea behind it is to have the kind
of preferred hand-crafted features in V1 and V2 areas.
The Algonauts Project 2021 Challenge: How the Human Brain Makes Sense of a
World in Motion (Cichy et al., 2021) focuses on event understanding from
videos, mainly to predict human brain responses for short video clips of
everyday events (e.g., panda eating, fish swimming, a person paddling). The
Algonauts Project 2021 Challenge had two tracks mini-track where the goal is
to predict brain activity in 9 ROIs of the visual brain (V1, V2, V3, V4, Body-
EBA, Face - FFA, STS, Object - LOC, Scene - PPA), the full-track goal is to
predict the whole-brain neural activity.
In this paper, we discuss the work performed on both tracks. The rest of this
paper is structured as follows: section 2 describes the dataset used in both
tracks: mini-track and full track, section 3 discusses the approaches used in
our study, and section 4 discusses the obtained results and analysis.

##  2 Dataset

The dataset provided contains 10102 3- seconds videos. The first 1000 videos
are considered as training set and are associated with fMRI human brain data
of 10 subjects in response to viewing muted videos from this set. The test set
is the last 102 3 seconds videos. For the mini-track, The data is provided for
9 regions of the visual brain (V1, V2, V3, V4, LOC, EBA, FFA, STS, PPA) in a
Pickle file (e.g. V1.pkl) that contains a num_videos x num_repetitions x
num_voxels matrix. For each ROI, while for the full track The data is provided
for selected voxels across the whole brain in a Pickle file (e.g. WB.pkl) that
contains a num_videos x num_repetitions x num_voxels matrix.

##  3 Materials and Methods

The aim of the challenge is to predict neural activity (fMRI responses) in the
visual cortex for 9 ROIs of the visual brain (V1, V2, V3, V4, Body- EBA, Face
- FFA, STS, Object - LOC, Scene - PPA) in the mini track challenge and to
predict the whole-brain neural activity (fMRI responses) in the full track
challenge. The most known approaches to predict fMRI responses are Voxel-wise
encoding models, ROI-wise encoding models. In Voxel-wise encoding model (Wu et
al., 2006; Naselaris et al., 2011), features are either hand-crafted (Gabor
Wavelet for V1,…etc) or extracted from well known CNNs (Pixels to feature
space). Then these features are either kept as is, or their dimensionality is
reduced. Those features are thought of as potential hypothesis features that
are generated or similar to the one generated in the brain region, represented
as a stimulus. Afterward, these features are linearly mapped onto each voxel’s
responses using a suitable computational model (linear regression, multi-layer
perceptron,…etc) Unlike the Voxel-wise encoding model where thousands of
regression models are constructed for several visual regions of interest
(ROIs), in ROI-wise encoding models, all voxels in one region of interest
(ROI) are jointly encoded. Two types of experiments for Stimulus-model-based-
encoding were conducted. The first approach is transfer learning of the deep
neural network to incorporate a pre-trained DNN and train a nonlinear mapping
from visual features to brain activity similar to what was discussed in (Zhang
et al., 2019). The second approach is following the traditional pipeline for
Voxel-wise encoding models.

###  3.1 Transfer learning for Stimulus prediction

The aim of the challenge is to predict neural activity responses to a set of
3-second videos, for the mini-challenge in the 9 ROIs or whole brain for the
full challenge. This experiment was conducted for the mini-challenge only.
Usually, for this type of experiment, the input is usually an image and its
corresponding stimulus. Since the input in this challenge is 3 seconds videos,
the challenge was how to perform the same task using non-video CNNs (as they
were hard to load and train using colab, without having notebook to crash even
for a small batch size). The aim was to build/finetune a network that
generates the stimulus for a given video.

The general process for transfer learning goes as follows:

  * •

A CNN network is trained on specific tasks and data set.

  * •

This CNN (base model) is chosen which is the state of the art in this specific
domain, or a model which has a near accuracy to the state of the art.

  * •

N-layers from this chosen model are copied to a target network (new network
with additional layers), in a new domain.

  * •

Train the new model in the new domain, while keeping weights of the first
N-layers fixed (i.e frozen) or finetune them.

The building process of our pipeline goes as follows:

  * •

AlextNet, and resnet-18 semi-supervised (Yalniz et al., 2019) models were
chosen as our candidate base models.

  * •

For the AlextNet, the first five convolutional layers, were copied (with 96,
256, 384, 384, and 256 kernels, respectively), while leaving the three fully
connected layers. For the resnet-18 semi-supervised model, all layers were
kept except for the fully connected layer which was then removed.

  * •

For the target network three variants were introduced:

    * –

Adding three fully connected layers after the base model. For AlextNet the
three fully connected layers were of size 4096, 4096, and number of stimuli
for the voxel in given region neurons. For the resnet-18 semi-supervised model
the three fully connected layers were of size 25088, 1024, and number of
stimuli for the voxel in given region neurons.

    * –

Adding Two LSTM layers followed by two fully connected layers. For the
AlextNet model, the two LSTM layers were bidirectional, with a hidden state of
512, and dropout of 0.2. The two fully connected layers of sizes 1024, number
of stimulus for the voxel in given region neurons.

    * –

Adding An three LSTM layers followed by two fully connected layers. The idea
behind it is that the stimulus is BOLD time series, therefore it might be
better to generate time series data directly from the features. For the
AlextNet model, the two LSTM layers were bidirectional, with a hidden state of
512, and dropout of 0.2. The last LSTM layer had a hidden state of the number
of stimuli for the voxel in given region neurons.

  * •

The input video is segmented into 16 frames, for each video, The 16 frames
images are inputted as a batch, and we have taken the mean values of their
prediction as the predicted stimulus for a given ROI.

  * •

The prediction dissimilarity between the predicted stimulus and the original
stimulus was used as a loss function for the network.

  * •

The layers of the base network were frozen, while we trained the additional
added layers in the target network.

  * •

the target model was trained for 10 epochs, we kept the best model version,
which had high correlation prediction in the validation set. We used 90-10
percent scheme as our training, validation policy.

  * •

Adam optimizer with learning rate 0.001 was used for training.

Based on a training dataset, voxel-wise encoding models can find the optimum
model for each voxel. However, because it is computationally impossible to
train a complicated non-linear model independently for each voxel, voxel-wise
modeling can only use a linear mapping between the feature and the brain
activity spaces. We used an ROI-wise encoding modeling strategy here, which
means we trained one model to predict the responses of all voxels in each ROI.
This method considerably decreases the training time and, more crucially, the
model parameters are jointly restricted by the prediction accuracy across all
voxels. There are multiple caveats in this system: training process is more
vulnerable to some noisy voxels, removing fully connected layers in the base
models, where fully connect layers in the base models usually are good
features for EBA, FFA, STS, LOC, PPA ROIs, and the optimal number of frames
per video. In early experiments, MSE loss in addition to dissimilarity metric
was used together, but they didn’t seem to perform well, on the training and
validation datasets.

###  3.2 Traditional pipeline for Voxel-wise encoding models

In this experiment several deep CNN models for features extraction were used,
in addition to that several computational model for generating voxels, were
tested for both challenges. VGG16, VGG19, resnet-18, resnet-18 semi-
supervised, resnet-18 semi weakly supervised, resnet-50 semi-supervised,
Nasnet mobile, AlexNet, Squeezenet, VOneNet resnset50 (Dapello et al., 2020),
and VOneNet Alexnet were used as our feature extractor. For the computational
models, Elastic net, lasso regression, linear regression, ridge regression,
and RES (Anderson et al., 2016) were used. Our pipeline goes as follows:

  * •

Each video in the training and test set was converted into batches of image
frames of size 15,10,16,26 per video.

  * •

For each batch, different layer activations for a given CNN model is
extracted.

  * •

These extracted features are then reduced in dimension using principal
component analysis (PCA) with 100 feature (100 feature was optimal number for
several CNNs and layers in training and validation set). Normalization is then
applied to the dataset.

  * •

For each ROI, the best feature (extracted from activation layer after applying
PCA and normalization) with high correlation in the validation dataset for
several subjects, is used for the training.

  * •

For choosing the best computational model, The best model with a given feature
and high correlation with respect to the validation set was chosen while
applying cross-validation of 3.

  * •

90-10 train-validation split scheme was used.

Multiple variants from this pipeline were introduced, where we tried to
combine 2 layers or more as features, generating a new feature matrix
consisting of all polynomial combinations of the features with a higher
degree, not applying PCA. However, the successful one was the pipeline
discussed above. As stated in our pipeline above: activation layer features
are either extracted from all CNN model layers or for a specific layers, for
each training and testing examples. Then PCA and normalization are applied. We
train multiple models for each subject and for each layer, for a specific ROI.
Then the best perform modeling for a specific layer for all subjects is chosen
for generating synthesized stimulus for the test set. For AlexNet model (which
consists of 8 layers, 5 convolutional layers, and three fully connected
layers) all layers were chosen for generating the features. For the ROIs,
layer 5 was used for whole-brain prediction, layer 2 was used for V1
prediction. For V2, V3, V4 layer 5 was used for prediction. For LOC, EBA, FFA,
PPA layer 8 was used, while for STS layer 6 is used. For resnet-18, resnet-18
semi-supervised, and resnet18- semi weakly supervised models we used the first
maxpool layer, four main blocks, and the fully connected layer as our feature
set. For the ROIs, the last fully connected layer was used for whole-brain
prediction, the third block was used for V1, V2, V3 regions. For V4 fourth
block was used, while for the remaining ROIs the last fully connected layer
was used. For resnet-50 and VOnet resnet-50 the last 15 Bottleneck layers were
used in addition to the last fully connected layer. For the ROIs, the last
Bottleneck was used for whole-brain prediction, in addition to V4, LOC, EBA,
FFA, PPA. For V1-V3 10th bottleneck layer was used, while for STS the 14th
bottleneck layer was used. For Nasnet mobile we used most of the layers for
generating features, resulting in 18 different features. For the ROIs, layer 4
was used for WB, V2, V3, V4, LOC, FFA, STS prediction. For V1 prediction layer
2 was used, while layer 8 was used for PPA prediction. Usually, the first
couple of layers are used for the prediction of the V1-V4 area, while later
layers in the model are used for prediction LOC, FFA, PPA, STS, WB, and the
pattern holds for most of the tested models.

##  4 Evaluation and Results

###  4.1 Evaluation

Evaluation for the test set on the leaderboard is carried out by comparing
predict brain responses to the empirically measured brain responses. The
comparison is carried out using Pearson’s correlation, comparing for each
voxel the 102-dimensional vector formed by the activations for the 102 test
set video clips. Then the correlation is normalized by the square root of the
corresponding voxel’s split-half reliability. These results in one value of
normalized correlation per voxel ranging from -1 to 1. Then the predictivity
is averaged across selected voxels in the brain full track, or across all the
voxels in each of the 9 brain regions of interest. For the model‘s evaluation
in the training and validation phase, Pearson’s correlation was used for
either a selected subject or multiple subjects for each ROI.

###  4.2 Results

Table 1 shows the achieved score for each model in the mini track, while table
2 shows the achieved score for each model in the full track. The best
performing model in the mini track was resnet-18 semi-supervised with lasso as
a regression model, while for the full track Nasnet mobile model with RES as a
model. Further analysis is conducted for the mini track results as shown in
figure 1, resnet18 semi-supervised with specific layer selection per ROI and
Lasso CV model has a higher correlation in V1, V2, Loc, and EBA regions, while
resnet50 semi-supervised with specific layer selection per ROI and Lasso CV
model performs well by having high correlation in V4, V3 areas. For FFA, STS,
and PPA areas, VOneNet resnset50 with specific layer selection per ROI and
Lasso CV model show a high correlation between the predicted stimulus and the
actual one. In the early stages in the development part, we have chosen the
model and the layer for each region, based on the one that shows a high
correlation. As shown in figure 2, there are several models that show better
performance in the validation set, however badly performs on the test set.
Therefore, it could be concluded that we cannot rely solely on the validation
set to choose candidate models and layers. Different approaches on Alexnet
model were analyzed on the test set, as shown in figure 3. AlexNet with
specific layer selection per ROI and Sparse linear regression shows better
correlation in V1, V2, and V3 areas, while for V4and EBA areas Alexnet
transfer learning three LSTM layers shows better results. For LOC, FFA, STS,
and PPA areas, the Alexnet transfer learning all fully connected shows a
better correlation. The interpretability and accuracy of an encoding model are
two important indicators to consider when evaluating it. The accuracy of a
visual encoding model indicates how well it can predict the brain activity
elicited by novel stimuli. The interpretability metric indicates how well we
can capture the relationship between the encoding model’s components (i.e.,
visual features) and the outcomes predicted by the model. Voxel-wise encoding
models show higher prediction accuracy and correlation in all brain ROIs.
However, it’s not clear when ROI-wise encoding models with non-linear mapping
outperforms voxel-wise encoding models. Most of the semi-supervised models and
the weakly supervised models show higher performance in most ROIs, which
suggests to uses such models features.

Method | Score
---|---
Alexnet + all layers as features + Sparse linear regression | 0.181348463
AlexNet + specific layer selection per ROI + Sparse linear regression | 0.4222287033
resnet18 + specific layer selection per ROI + Sparse linear regression | 0.4554744991
resnet18 + specific layer selection per ROI + MultiTaskElasticNetCV | 0.503842829
Alexnet transfer learning all fully connected | 0.4318425715
Alexnet transfer learning three LSTM layers | 0.4328641541
resnet18 transfer learning all fully connected | 0.3986074061
Alexnet transfer learning two LSTM layers and two fully connected layers | 0.433419799
resnet18 + specific layer selection per ROI +RES model | 0.5000028286
Nasenet mobile + no PCA + specific layer selection per ROI + RES model | 0.4999065559
VGG16 bn + specific layer selection per ROI + Lasso CV model | 0.0578059194
resnet18 semi weakly supervised + specific layer selection per ROI + Lasso CV model | 0.5552126635
resnet18 semi-supervised + specific layer selection per ROI + Lasso CV model | 0.5673601542
resnet18 semi weakly supervised + specific 2 layers selection per ROI + RES model | 0.5113630713
resnet18 semi weakly supervised + higher dimension features + RES model | 0.5052717458
resnet50 semi-supervised + specific layer selection per ROI + Lasso CV model | 0.5637263751
Squeezenet + specific layer selection per ROI + Lasso CV model | 0.4994109545
VOneNet resnset50 + specific layer selection per ROI + Lasso CV model | 0.5307863683
VOneNet Alexnet + specific layer selection per ROI + Lasso CV model | 0.4756440395
Table 1: Results for mini-track (9 ROIs), scoring is based on Pearson’s correlation, resnet-18 semi-supervised outperform all other model in the table based on correlation score Method | Score
---|---
Alexnet + all layers as features + Sparse linear regression | 0.1229460643
AlexNet + specific layer selection per ROI + Sparse linear regression | 0.1893032764
resnet18 + specific layer selection per ROI + Sparse linear regression | 0.196156364
Nasenet mobile + no PCA + specific layer selection per ROI + RES model | 0.2640751352
VGG19 + specific layer selection per ROI +RES | 0.0149241953
resnet18 semi weakly supervised + specific 2 layers selection per ROI + RES | 0.2503818611
resnet18 semi-supervised + specific 2 layers selection per ROI + RES model | 0.2496098364
resnet50 semi-supervised + specific layer selection per ROI + RES model | 0.2613774908
VOneNet resnset50 + specific layer selection per ROI + RES model | 0.2491422229
Table 2: Results for the full-track (Whole-Brain), scoring is based on
Pearson’s correlation, resnet-18 semi weakly-supervised outperform all other
models in the table based on correlation score

##  5 Conclusion

In this paper, the results and the main findings of the Algonauts Project 2021
Challenge: How the Human Brain Makes Sense of a World in Motion were
presented, in which different experiments were carried out using two
approaches: voxel-wise encoding model, and ROI-wise encoding models. In voxel-
wise encoding methods semi-weakly supervised models and semi-supervised models
with regularized regression seem to achieve high performance, while in ROI-
wise encoding models, the model seems to be disturbed by noise in the voxel
readings. Future work will include investigating more models, layers, and
better validation techniques for voxel-wise encoding models, while different
loss functions and regularization will be investigated for ROI-wise encoding
models.

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Figure 1: Comparison between different model with respect to the 9 ROIs in the
mini track in the test set Figure 2: Comparison between different model with
respect to the 9 ROIs in the mini track in the validation set for subject 4
Figure 3: Comparison between different approaches used in Alexnet model


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TXTaffil

# Systematic study of the experimental measurements on ratios of different
$\Upsilon$ states

Wangmei Zha<EMAIL_ADDRESS>University of Science and Technology of
China, Hefei, China  Brookhaven National Laboratory, New York, USA  Chi Yang
University of Science and Technology of China, Hefei, China  Brookhaven
National Laboratory, New York, USA  Bingchu Huang  Brookhaven National
Laboratory, New York, USA  Lijuan Ruan  Brookhaven National Laboratory, New
York, USA  Shuai Yang  University of Science and Technology of China, Hefei,
China  Brookhaven National Laboratory, New York, USA  Zebo Tang  University of
Science and Technology of China, Hefei, China  Zhangbu Xu  Brookhaven National
Laboratory, New York, USA

###### Abstract

The world data on yields and ratios of different $\Upsilon$ states created in
hadron collisions at $\sqrt{s}=19-8000$ GeV are examined in systematic way. We
find that $\Upsilon(2S)/\Upsilon(1S)=0.275\pm 0.005$ and
$\Upsilon(3S)/\Upsilon(1S)=0.128\pm 0.004$. No signficant energy dependence of
these ratios are observed within the broad collision energies. In addition,
the rapidity, transverse momentum, and transverse mass dependence of these
ratios are also reported.

##  I Introduction

Current data at RHIC demonstrate rapidly thermalizing matter characterized by:
1) initial energy densities far above the critical values predicted by lattice
QCD for formation of a Quark Gluon Plasma (QGP); 2) opacity to jets; and 3)
nearly perfect fluid flow, which is marked by constituent interactions of very
short mean free path, established most probably at a stage preceding hadron
formation starwhitepaper . One of the important next objectives is to study
the color screening length in QGP rhicIIQuarkonia . Constituent heavy quark-
antiquark pairs in quarkonia are subject to color screening and should be
dissolved at high temperature. The dissociation temperatures of different
species will vary due to different radii and binding energies. The precise
measurements of transverse momentum ($p_{T}$) distributions of quarkonia for
different centralities, collision systems, and energies will serve as a
thermometer of the QGP.

$J/\psi$ is the most studied quarkonium at the RHIC and LHC. In central
collisions, $J/\psi$ is less suppressed in Pb+Pb at 2.76 TeV for
$2.5\\!<|y|\\!<4$ than in Au+Au collisions at 200 GeV for $1.2<|y|<2.2$
phenixjpsi ; ALICEjpsi . A similar feature is observed for mid-rapidity
comparisons between LHC and RHIC energies. Comparisons to model calculations
indicate that recombination plays a significant role at RHIC and a more
significant role at LHC. Furthermore, the $p_{T}$ dependence of $J/\psi$
suppression ALICEjpsi ; phenixjpsi:07 ; starjpsi:12 , the flow pattern of
$J/\psi$ as a function of $p_{T}$ Yang:12 ; starjpsiv2 , and the high $p_{T}$
$J/\psi$ suppression pattern as a function of centrality starjpsi:12 ; Moon:12
, reported at LHC and RHIC, can be described consistently by model
calculations incorporating color screening and recombination features (See a
recent review article for details GaleRuan:12 ).

Besides $J/\psi$, the different $\Upsilon$ states are also ideal tools for
this study since the ground state and excited states melt at different
temperatures and all of them could decay to dileptons. Furthermore, since the
$b\bar{b}$ cross section at RHIC energy is expected to be two orders of
magnitude smaller than $c\bar{c}$ cross section from FONLL calculations vogtum
, the recombination contribution from QGP phase might be negligible to
bottomonium production, at least at RHIC. Meanwhile, the $\Upsilon$ absorption
cross sections with the abundantly produced hadrons in these collisons are
relatively small according to model calculation nuclear absorption ,
therefore, suppression from the absorption effect is expected to be
unimportant. These make $\Upsilon$ an even better probe for studying the color
screening effect in QGP if sufficient statistics can be achieved
experimentally.

In addition to its important role in studying the color screening effect, a
measurement of the $\Upsilon(1S,2S,3S)$ states in $p+p$ and heavy ion
collisons can help to set limits on the medium temperature created in heavy-
ion collisions, because the sequential suppression pattern of the excited
states is sensitive to the temperature reached in the medium sequential
suppression . The nuclear modification factor $R_{AA}$, which can quantify the
suppression of particle production in nuclear collisons, is defined as the
ratio of the inclusive hadron yield in nuclear collisions to that in $p+p$
collisions scaled by the underlying number of binary nucleon-nucleon
collisions. Measurements at CMS show that $R_{AA}$[$\Upsilon$(1S)] is 0.4-0.5
while $R_{AA}$[$\Upsilon$(2S)] is 0.1 in central Pb+Pb collisions at 2.76 TeV
cmsupsilon:12 . At RHIC 200 GeV, $R_{AA}$[$\Upsilon$(1S+2S+3S)] is about 0.4
in central Au+Au collisions Trzeciak:12 . Considering feeddown contributions [
50% for $\Upsilon$(1S) ], measurements at RHIC and LHC indicate that
$\Upsilon$(3S) is completely melted and that $\Upsilon$(2S) is strongly
suppressed in central A+A collisions.

With bremsstrahlung radiation of electrons traversing the detector material,
the STAR experiment is at the borderline of being able to separate the three
states. The muons in $\Upsilon$ do not suffer from this degradation. The Muon
Telescope Detector (MTD) at STAR to be completed in 2013 will provide
excellent muon identification capabilities and thus enable the measurements of
different $\Upsilon$ states mtd  through $\Upsilon\rightarrow\mu^{+}\mu^{-}$
to estimate the medium temperature created at RHIC. In the RHIC-II era, with
the full MTD system at STAR, we will be able to measure different $\Upsilon$
states with good precision by taking advantage of the high luminosity in Au+Au
collisions. While in 200 GeV $p+p$ collisions which can provide the reference
data for $R_{AA}$ calculation, the $\Upsilon(3S)$ total cross section
measurement with 10% statistical uncertainty on total cross section requires
sample 400 $pb^{-1}$ luminosity, which may not be allowed by the run plan. On
the other hand, different $\Upsilon$ states have been measured from low to
high energy and we may use the previous measurements to derive the baseline of
their ratios for the corresponding heavy ion collisions. In this article, we
study the world-wide data and obtain different $\Upsilon$ state ratios versus
energy.

##  II Results

Measurements of the $\Upsilon$ production have been performed by many
experiments J. Badier:NA3 ; J.K. Yoh ; W.R. Innes ; K. Ueno ; S. Childress ;
G. Moreno:E605 ; T. Yoshida:E605 ; P.L. McGaughey:E772 ; T. Alexopoulos:E771 ;
L. Camilleri:R-108 ; C. Kourkoumelis ; A.L.S. Angelis:CCOR ; C. Albajar:UA1 ;
F. Abe:CDF ; Upsilon:CMS ; Upsilon:LHCb ; Upsilon:ATLAS ; Upsilon:E886 ;
Upsilon:LHCb8TeV  in the wide range of the proton-nucleon center-of-mass
energy $\sqrt{s}$ of 19 to 8000 GeV, and with targets ranging from proton (A =
1) to platinum (A = 195) with both proton and antiproton beams. Only few
experiments could allow precise measurements of the dilepton mass spectrum in
the range of 8-15 GeV/$c^{2}$ and seperation of the three lowest-mass
$\Upsilon$ states J.K. Yoh ; K. Ueno ; T. Yoshida:E605 ; G. Moreno:E605 ;
Upsilon:E886 ; F. Abe:CDF ; Upsilon:CMS ; Upsilon:LHCb ; Upsilon:ATLAS ;
Upsilon:LHCb8TeV . We explore the $p_{T}$, rapidity, and transverse mass
($m_{T}$) dependence of $\Upsilon(2S)$ and $\Upsilon(3S)$ production relative
to the $\Upsilon(1S)$ by deriving the ratios with n=2,3, defined as following:

$\frac{\Upsilon(nS)}{\Upsilon(1S)}=\frac{\sigma[p(\bar{p})+p(A)\rightarrow\Upsilon(nS)]\times
Br[\Upsilon(nS)\rightarrow
l^{+}l^{-}]}{\sigma[p(\bar{p})+p(A)\rightarrow\Upsilon(1S)]\times
Br[\Upsilon(1S)\rightarrow l^{+}l^{-}]}$ (1)

where $\sigma[p(\bar{p})+p(A)\rightarrow\Upsilon(nS)]$ (n=1,2,3) is the
$\Upsilon(nS)$ cross section in $p(\bar{p})+p(A)$, $Br[\Upsilon(nS)\rightarrow
l^{+}l^{-}]$ is the dilepton branching ratio of the corresponding $\Upsilon$
states. Such observables are sensitive to the magnitude and kinematic
dependencies of feed-down contributions between the three $\Upsilon$ states.
Production yields of quarkonium states could be modified from $p(\bar{p})+p$
to $p(\bar{p})+A$ collisions by cold nuclear matter effects R.Vogt . However,
such effects should have a small impact on the ratios. The nuclear
modifications of the parton distribution functions should have an equivalent
effect on the three $\Upsilon$ states, because partons involved into the
production have similar kinematics. Nuclear dependence of $\Upsilon$
production measured at E772 Upsilon:E772  and E886 Upsilon:E886  indicates
that no nuclear dependence difference,within uncertainties, is observed
between the $\Upsilon(1S)$ and the sum of $\Upsilon(2S+3S)$.

experiment | system | energy (GeV) | rapidity | $\Upsilon(2S)/\Upsilon(1S)$ | $\Upsilon(3S)/\Upsilon(1S)$ | $\Upsilon(2S+3S)/\Upsilon(1S)$ | ref.
---|---|---|---|---|---|---|---
CFS $\triangledown$ | $p+p$ | $19.4$ | $<y>_{ac}=0.40$ | $0.670\pm 0.940$ | $0.100\pm 0.600$ | $0.770\pm 1.115$ |  J.K. Yoh
CFS $\triangledown$ | $p+p$ | $23.7$ | $<y>_{ac}=0.21$ | $0.460\pm 0.130$ | $0.000\pm 0.080$ | $0.460\pm 0.157$ |  J.K. Yoh
CFS $\triangledown$ | $p+p$ | $27.4$ | $<y>_{ac}=0.03$ | $0.380\pm 0.110$ | $0.080\pm 0.060$ | $0.460\pm 0.122$ |  J.K. Yoh
CFS $\vartriangle$ | $p+P_{t}$ | $27.4$ | $y=0$ | $0.310\pm 0.030$ | $0.150\pm 0.020$ | $0.460\pm 0.034$ |  K. Ueno
E605 $\blacktriangle$ | $p+B_{e}$ | $38.8$ | $y=0$ | $0.310\pm 0.110$ | $0.090\pm 0.060$ | $0.400\pm 0.125$ |  T. Yoshida:E605
E605 $\lozenge$ | $p+C_{u}$ | $38.8$ |  $-0.15\\!<x_{F}\\!<0.25$ ($-0.28\\!<y\\!<0.46$) | $0.270\pm 0.011$ | $0.131\pm 0.008$ | $0.400\pm 0.014$ |  G. Moreno:E605
E886 $\square$ | $p+d$ | $38.8$ |  $0\\!<x_{F}\\!<0.6$ ($0.00\\!<y\\!<0.98$) | $0.321\pm 0.012$ | $0.127\pm 0.009$ | $0.448\pm 0.016$ |  Upsilon:E886
E886 $\bigcirc$ | $p+p$ | $38.8$ |  $0\\!<x_{F}\\!<0.6$ ($0.00\\!<y\\!<0.98$) | $0.274\pm 0.017$ | $0.134\pm 0.013$ | $0.408\pm 0.022$ |  Upsilon:E886
CDF $\blacktriangledown$ | $p+\bar{p}$ | $1800$ | $|y|\\!<0.4$ | $0.281\pm 0.048$ | $0.155\pm 0.032$ | $0.436\pm 0.058$ |  F. Abe:CDF
CMS $\bullet$ | $p+p$ | $7000$ | $|y|\\!<2.0$ | $0.258\pm 0.012$ | $0.138\pm 0.010$ | $0.396\pm 0.015$ |  Upsilon:CMS
LHCb $\blacklozenge$ | $p+p$ | $7000$ | $2.0\\!<y\\!<4.0$ | $0.245\pm 0.015$ | $0.124\pm 0.008$ | $0.369\pm 0.020$ |  Upsilon:LHCb
ATLAS $\blacksquare$ | $p+p$ | $7000$ | $|y|\\!<2.25$ | $0.256\pm 0.019$ | $0.115\pm 0.010$ | $0.371\pm 0.024$ |  Upsilon:ATLAS
LHCb $\bigstar$ | $p+p$ | $8000$ | $2.0\\!<y\\!<4.5$ | $0.256\pm 0.005$ | $0.125\pm 0.003$ | $0.381\pm 0.006$ |  Upsilon:LHCb8TeV
Table 1: (color online) $\Upsilon(2S)/\Upsilon(1S)$,
$\Upsilon(3S)/\Upsilon(1S)$ and $\Upsilon(2S+3S)/\Upsilon(1S)$ in different
experiments. Figure 1: (color online) Ratios of $\Upsilon(2S)/\Upsilon(1S)$
and $\Upsilon(3S)/\Upsilon(1S)$ as a function of rapidity (or feyman scale)
measured by E886, ATLAS and LHCb experiments. The error bars represent the
quadrature sum of statistical and systematic uncertainties.

Figure 1 shows the ratios of $\Upsilon(2S)/\Upsilon(1S)$ and
$\Upsilon(3S)/\Upsilon(1S)$ as a function of $\Upsilon$ rapidity (or Feynman
scaling variable $x_{F}$).The LHCb 7 TeV Upsilon:LHCb , 8 TeV Upsilon:LHCb8TeV
and ATALS Upsilon:ATLAS  results are measured as a function of rapidity. The
universal rapdity independent ratios for both $\Upsilon(3S)/\Upsilon(1S)$ and
$\Upsilon(2S)/\Upsilon(1S)$ are observed from these three experiments within
their rapidity coverage. For fixed target experiments Upsilon:E886 ; G.
Moreno:E605 , the ratios are extracted as a function of $x_{F}$. Taking the
uncertainties into account, we can not claim any $x_{F}$ dependence of the
ratios for both $\Upsilon(2S)/\Upsilon(1S)$ and $\Upsilon(3S)/\Upsilon(1S)$.
These ratio values are almost the same as those measured at LHC despite the
huge center-of-mass energy difference.

Figure 2: (color online) Ratios of differential $\Upsilon(2S)/\Upsilon(1S)$
and $\Upsilon(3S)/\Upsilon(1S)$ as a function of transverse momentum measured
in world-wide experiments.The error bars represent the quadrature sum of
statistical and systematic uncertainties.

Figure 2 depicts the ratios of $\Upsilon(2S)/\Upsilon(1S)$ and
$\Upsilon(3S)/\Upsilon(1S)$ as a function of $p_{T}$. The measured
$\Upsilon(2S,3S)/\Upsilon(1S)$ ratios at ATLAS Upsilon:ATLAS  are relatively
constant in the $0\\!<p_{T}\\!<5$ GeV/$c$ range. At higher $p_{T}$ a
significant and steady rise in the relative production rates of higher
$\Upsilon$ states is observed. The measured results at CMS Upsilon:CMS  and
LHCb Upsilon:LHCb ; Upsilon:LHCb8TeV  follow the same trend as that of ATLAS
for the corresponding $p_{T}$ ranges. The fixed target measurements
Upsilon:E886  seem different in their $p_{T}$ coverage ($0\\!<p_{T}\\!<3.5$
GeV/$c$) for $\Upsilon(2S)/\Upsilon(1S)$, which decreases with $p_{T}$.

Figure 3: (color online) Ratios of $\Upsilon(2S)/\Upsilon(1S)$ and
$\Upsilon(3S)/\Upsilon(1S)$ as a function of $m_{T}$ measured in world-wide
experiments. The error bars represent the quadrature sum of statistical and
systematic uncertainties.

Figure 3 shows the ratios of $\Upsilon(2S)/\Upsilon(1S)$ and
$\Upsilon(3S)/\Upsilon(1S)$ as a function of $m_{T}$. The results at LHCb
Upsilon:LHCb ; Upsilon:LHCb8TeV , CMS Upsilon:CMS , ATLAS Upsilon:ATLAS , and
CDF F. Abe:CDF  all follow the same trend. The ratios first decrease and then
increase with the increasing $m_{T}$.

Figure 4: (color online) Ratios of $\Upsilon(2S)/\Upsilon(1S)$,
$\Upsilon(3S)/\Upsilon(1S)$ and $\Upsilon(2S+3S)/\Upsilon(1S)$ as a function
of center-of-mass energy measured in world-wide experiments.The error bars
represent the quadrature sum of statistical and systematic uncertainties.

Figure 4 and Table 1 show the $\Upsilon(2S)/\Upsilon(1S)$,
$\Upsilon(3S)/\Upsilon(1S)$, and $\Upsilon(3S+2S)/\Upsilon(1S)$ as a fuction
of center-of-mass energy using the experimental measurements of the three
$\Upsilon$ states J.K. Yoh ; K. Ueno ; T. Yoshida:E605 ; G. Moreno:E605 ;
Upsilon:E886 ; F. Abe:CDF ; Upsilon:CMS ; Upsilon:LHCb ; Upsilon:ATLAS . The
ratios with the same center-of-mass energy have been shifted slightly for
clarity in the figure. As shown in Table 1, the center-of-mass energy points
are for 19.4 GeV, 23.7 GeV, 27.4 GeV, 38.8 GeV, 1.8 TeV, and 7 TeV. The energy
points with relatively precise ratios are 38.8 GeV, 1.8 TeV, and 7 TeV. The
ratios measured at these three energy points are almost the same and show no
energy dependence despite the huge center-of-mass energy difference. The
constant fit results are $\Upsilon(2S)/\Upsilon(1S)=0.275\pm 0.005$ and
$\Upsilon(3S)/\Upsilon(1S)=0.128\pm 0.004$. This provides much more precise
reference ratios in 200 GeV $p+p$ collisions.

##  III Summary

We study the world-wide data of different $\Upsilon$ states at
$\sqrt{s}=19-8000$ GeV. We find that $\Upsilon(2S)/\Upsilon(1S)=0.275\pm
0.005$ and $\Upsilon(3S)/\Upsilon(1S)=0.128\pm 0.004$. No signficant energy
dependence of these ratios are observed within the broad collision energies.
In addtion, we observed no significant rapidity dependence of these ratios
within the broad collision energies. The $m_{T}$ dependence of these ratios
measured in LHC and CDF follow the same trend. The $p_{T}$ trend of the
$\Upsilon(2S)/\Upsilon(1S)$ ratios seem different from each other in the
region $0\\!<p_{T}\\!<3.5$ GeV/$c$ between LHC results and fixed target
results.

##  IV Acknowledgments

We express our gratitude to the STAR Collaboration and the RCF at BNL for
their support. This work was supported in part by the U.S. DOE Office of
Science under the contract No. DE-AC02-98CH10886; authors Wangmei Zha and Chi
Yang are supported in part by the National Natural Science Foundation of China
under Grant Nos 11005103 and 11005104.

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