# Chaining thoughts and LLMs to learn DNA structural biophysics

Tyler D. Ross
Department of Physics
MIT
<EMAIL_ADDRESS>
&Ashwin Gopinath
Department of Mechanical Engineering
MIT
<EMAIL_ADDRESS>

###### Abstract

The future development of an AI scientist, a tool that is capable of
integrating a variety of experimental data and generating testable hypotheses,
holds immense potential. So far, bespoke machine learning models have been
created to specialize in singular scientific tasks, but otherwise lack the
flexibility of a general purpose model. Here, we show that a general purpose
large language model, chatGPT 3.5-turbo, can be fine-tuned to learn the
structural biophysics of DNA. We find that both fine-tuning models to return
chain-of-thought responses and chaining together models fine-tuned for
subtasks have an enhanced ability to analyze and design DNA sequences and
their structures.

##  1 Introduction

With the ever growing accumulation of experimental data across vast fields of
science, it has become clear that a machine learning model that is capable of
integrating all this data and generating new hypotheses would revolutionize
the advancement of scientific knowledge. Specialized models have been created
to search for new physics [1] or predict the structures of proteins [2].
However, the recent success of general purpose large language models (LLMs)
have shown that a single model is capable of performing a wide range of tasks,
such as programming, translation, and summarization. The textual
representation that is typically used to represent amino and nucleic acid
polymers appears well-suited for LLM frameworks. In fact, recent studies have
shown that the transformer architecture of LLMs can also be utilized in
constructing specialized models to predict the structures of biomolecules [3,
4, 5]. However, as a small step toward the goal of an interdisciplinary AI
scientist, we are interested in determining if a general purpose LLM can be
fine-tuned to model a physical phenomenon. Specifically, we aim to test if
chatGPT 3.5-turbo can learn the biophysics of DNA structure formation.

The structural biophysics of nucleic acids forms the basis of DNA
nanotechnology, which harnesses the predictable nature of DNA base pairing and
molecular self-assembly to create complex nanostructures as well as perform
computations [6, 7, 8, 9]. A key component to DNA nanotechnology is the
formation of secondary structures, which are the specific shapes or
arrangements that DNA molecules can assume beyond the familiar double helix of
the primary structure. Secondary structures are largely governed by two
phenomena, the first being Watson-Crick base pairing between DNA’s four
nucleotides: adenine (A), thymine (T), cytosine (C), and guanine (G). Adenine
pairs with thymine (A-T) and cytosine pairs with guanine (C-G) through highly
specific hydrogen bonding. Notably, C-G bonds are more energetically favorable
than A-T bonds. Base pairing is dependent on the directionality of the DNA
strand, denoted as 5’ (five-prime) to 3’ (three-prime) ends. Reverse
complements are sequences that would bind to each other when aligned in
opposite directions. For instance, the sequence 5’-AGTC-3’ would have a
reverse complement of 5’-GACT-3’. Beyond base pairing, there is also an
attraction between paired bases in the form of stacking bonds. As with base
pairing, the strength of stacking bonds varies as a function of the base pairs
involved. The likelihood of a given structure forming at thermodynamic
equilibrium is determined by its free energy. The free energy of a DNA
structure is typically approximated by a nearest neighbor model that uses the
energies of pairwise stacking bonds, which have been determined empirically,
plus the energy from base pairing.

These energetic approximations are the basis of the NUPACK software suite [10,
11], which is the standard in the DNA nanotech community for the analysis and
design of DNA and RNA structures. NUPACK predicts the most stable structure
that will form for a given set of DNA strands by finding the structure that
has the minimum free energy (MFE) of all possible structures (up to a user-
designated complex size limit). The DNA secondary structures are represented
using parens-dot-plus notation, which uses parentheses to indicate base paired
regions, dots for unpaired nucleotides, and pluses to separate multiple
strands. For example, “((((..+….))))” represents two strands where the first
four bases of strand 1 are bound to the last four bases of strand 2. For this
work, we will be using NUPACK to provide the data for training and validation.
It is worth emphasizing, however, that NUPACK is not a complete biophysical
model. For example, psudoknoted structures as well as Hoogsteen base pairing,
which allows for the formation of triplexs and quradraplexs, are both ignored.
In this work, we will be using a simplified data set, where DNA pairs are of
equal length and are not self-complementary (i.e. the strands do not bind to
themselves). This allows us to separate out the capability of the LLMs to
learn the fundamentals of DNA structural biophysics from the task of searching
across the space of all possible configurations.

##  2 Methods

Figure 1: Schemes for chain of thought (CoT) and pipelines of models used to
perform sequence analysis and design. a, Chain of thought fine-tuning where
the model prints out each base and their neighbors before determining if a
stable base pair is formed. b, A sequence analysis pipeline that uses a model
that is tuned to provide the reverse complement of a sequence, which is then
fed into a model that is tuned to determine the secondary structure. Boxes in
white indicate values provided by the user, teal boxes are fine-tuned models,
and orange boxes represent final answers from model outputs. c, Expert-based
error checking scheme where the sequences designed by one model are analyzed
by another to verify that the desired secondary structure is formed.

Our work is built on two primary concepts: fine-tuning models to follow a
train of thought approach before arriving at an answer, and using a pipeline
of models (experts) to solve different aspects of the problem and provide
feedback.

For simplicity in implementation, each expert is a fine-tuning of
gpt-3.5-turbo-1106 using OpenAI’s API. A basic error checking step is applied
to the output of each expert, where the model is queried with the same input
(up to 20 times) if the model’s final answer is not the expected length or
contains invalid characters. Models fine-tuned to follow a chain-of-thought
(CoT) approach will step-by-step print out the nearest neighbor window of the
input while assembling the structure/sequence pair before giving their final
answers (Fig. 1a). In addition to breaking down the problem into simpler steps
as shown in [12], our fine-tuned CoT approach leverages a feature of our
problem (i.e. that binding stability is based on nearest neighbor
interactions) to give the model a hint as to how to process the input. When
the nearest neighbor window is applied, the input string(s) are padded with
the character “_” to indicate the ends of the sequences, as bases at the edges
are less likely to form stable base pairs due to having only one potential
stacking bond. For the CoT approach, we only evaluate a model’s performance
based on its final answer, which comes after “ans:”.

In all of our experiments we explore the utilization of an expert pipeline
where models that have been fine-tuned to perform subtasks feed into each
other. Here we are motivated by the idea that a collection of models that are
specialized on subtasks can perform better than a single model [13]. In the
simplest case, we have the output of one model provide part of the input to
another model (Fig. 1b). For the more complex problem of sequence design, we
introduce an error checking scheme where the sequences generated by one model
are analyzed to see if they form the desired secondary structure (Fig. 1c). If
the structures do match then the sequences are accepted.

The ground truth data used to train and validate the models is created using
NUPACK. The sequences are designed by NUPACK to ensure that the MFE structure
does not have self-complementarity or require alignment. For sequence design,
we use NUPACK to determine the ground truth MFE structure formed by the LLM
designed sequences. We set NUPACK’s model conditions to 20 ∘C, 1 M sodium, and
with ensemble stacking. Sequences are of lengths between 10-25 bases with
sequence pairs being of matching length. Paired strands have a minimum of 1
mismatch up to 30% of bases mismatched. The training set size is 10,000 and
validated against a set of 1,000 sequences. Learning curves are generated over
training sets containing 200, 500, 1,500, 3,700, and 10,000 examples. When
evaluating the learning curves for the pipelines, all experts are fine-tuned
on data sets of the same size. A separate training and validation set is used
for the sequence design model, where each entry in the set is a unique
structure.

##  3 Experiments and results

###  3.1 Predicting secondary structure

We begin exploring the capability of a general purpose LLM to learn the
secondary structure of DNA by testing four different approaches: naive, chain-
of-thought (CoT), reverse complement followed by CoT, and a pipeline of a
reverse complement expert feeding into a secondary structure expert. The naive
approach is to provide two DNA sequences and have the model return the
corresponding secondary structure in dot-parens-plus notation. For example,
Input: “ACCGCGCCCT TGGGCGGGGA” Output: “.((.(((((.+.))))).)).”. For CoT, the
input remains the same but the output applies a nearest neighbor window as it
determines the structure, Input: “CCCGGCGCTG CTGCGGCGGG” Output: “[_CC,_GG]:(
[CCC,GGG]:(( [CCG,GGC]:((( [CGG,GCG]:(((( [GGC,CGG]:((((. [GCG,GGC]:((((.(
[CGC,GCG]:((((.(( [GCT,CGT]:((((.((( [CTG,GTC]:((((.(((. [TG_,TC_]:((((.(((..
ans:((((.(((..+..))).))))”. We next vary the CoT approach by breaking the
problem down further. The models so far had to recognize that the relationship
between the strands is from left to right on the first sequence and from right
to left on the second sequence and that further it must learn the pairing rule
of G-C and T-A all within one step. We therefore introduce a third condition
where the model first produces the reverse complement of the second sequence
and then performs a CoT base comparison between the first sequence and the
reverse complement of the second sequence. For example, Input: “GCAGGCCCGAA
AACGGGGCTGC” Output: “GCAGCCCCGTT [_GC,_GC]:( [GCA,GCA]:(( [CAG,CAG]:(((
[AGG,AGC]:(((( [GGC,GCC]:((((. [GCC,CCC]:((((.( [CCC,CCC]:((((.((
[CCG,CCG]:((((.((( [CGA,CGT]:((((.(((( [GAA,GTT]:((((.((((.
[AA_,TT_]:((((.((((.. ans:((((.((((..+..)))).))))”. Finally, we break the
problem down even further by creating a pipeline where a separate model is
responsible for determining the reverse complement and sends it to another
model that determines the secondary structure. For example, first we provide
the reverse complement expert with sequence 2: “GGCCGCCGAC” and receive its
reverse complement “GTCGGCGGCC”, we then give the secondary structure expert
the Input: “GTCGGCGGGC GTCGGCGGCC” Output: “[_GT,_GT]:( [GTC,GTC]:((
[TCG,TCG]:((( [CGG,CGG]:(((( [GGC,GGC]:((((( [GCG,GCG]:((((((
[CGG,CGG]:((((((( [GGG,GGC]:(((((((( [GGC,GCC]:((((((((. [GC_,CC_]:((((((((.(
ans:((((((((.(+).))))))))”. For comparison, we also run this pipeline where a
reverse complement algorithm provides the ground truth reverse complement to
the secondary structure expert.

| naive | CoT |  | rev. comp.
---
& CoT
| pipeline
---
rev. comp. expert
$\rightarrow$ CoT
| pipeline
---
ground truth
rev. comp.
$\rightarrow$ CoT
accuracy % | 7.4 | 77.4 | 88.9 | 92.8 | 95.4
Table 1: Secondary structure prediction accuracy. Figure 2: Learning curves
for secondary structure prediction and the reverse complement expert. For the
secondary structure, we are using the expert pipeline approach.

Results The general trend we find is that the more we break down the problem
the better the performance (Table 1). In all cases the majority of errors are
due to incorrect base pairing rather than issues with formatting or incorrect
structure lengths. Having the model explicitly write out the nearest neighbor
window results in a substantial improvement over the naive approach. The
benefit of CoT here presumably comes from both expanding the context before
the answer is given and, more specifically, by breaking down the relevant
character relationships. It is perhaps surprising how large an improvement we
see when the model produces the reverse complement of the second sequence
before performing CoT. The comparison of one sequence from left-to-right with
another sequence from right-to-left may be inherently difficult for the model
to learn given the unidirectional nature of the transformer decoder
architecture. Producing the reverse complement first instead allows the model
to compare both strings from left to right. For the pipeline approach, we
additionally fine-tune a model to return the reverse complement of a sequence,
which has an accuracy of 98.4$\%$. We note that, unlike the determination of
the secondary structure, finding the reverse complement of a sequence follows
a simple closed-form function. Perhaps this is why the reverse complement
expert saturates at small training sizes in comparison to the secondary
structure model (Fig. 2). The difference in the performance between the expert
pipeline and the ground truth pipeline suggests that there is largely no
overlap in where errors occur for the structure and reverse complement
experts. Therefore, there may be a diminishing return in terms of the number
of experts a pipeline uses. Ultimately, offloading the reverse complement
operation to another model enhances the accuracy of the secondary structure
prediction.

###  3.2 Calculating minimum free energy

To further test the model’s ability to learn the structural physics of DNA, we
ask it to calculate the minimum free energy (MFE) for a pair of sequences. As
mentioned in the Introduction, the free energy is approximated as a function
of both the base pairing and the nearest-neighbor stacking bond energies,
which are empirically determined. Here we challenge the model to find the MFE
without explicitly writing out any mathematical operations. We explore MFE
calculation across four approaches: naive, reverse complement followed by CoT,
a pipeline where a model provides the reverse complement to a CoT MFE model,
and a variation on the naive approach where the model is provided with both
the ground truth reverse complement and ground truth secondary structure. The
first three cases are nearly identical to what is described in the previous
section, but on the last step the model returns the MFE instead of the
structure. Also as before, we test the pipeline method where the reverse
complement expert is substituted for a ground truth algorithm. An example of
the ground truth reverse complement and structure approach is as follows,
Input: “CGTTTTTCCGACTTGCGCCG CGAATTTCCGACGTGCGCCG
((..((((((((.(((((((+))))))).))))))))..))” Output: “-28.3”. The idea here is
to test if providing the model with the secondary structure as part of the
input is sufficient to match the model’s performance over the CoT approach.

| naive |  | rev. comp.
---
& CoT
| pipeline
---
rev. comp. expert
$\rightarrow$ CoT
| pipeline
---
ground truth
rev. comp.
$\rightarrow$ CoT
| ground truth
---
rev. comp.
& ground truth
structure
error $\left(\frac{\text{kcal}}{\text{mol}}\right)$ | 1.67 $\pm$ 1.43 | 1.55 $\pm$ 1.83 | 1.23 $\pm$ 1.63 | 1.15 $\pm$ 1.26 | 1.43 $\pm$ 1.19
Table 2: Minimum free energy error from sequence analysis. Error is mean
absolute error and the $\pm$ term represents standard deviation of the
absolute error. Figure 3: Impact of training set size on MFE predictions for
the reverse complement expert pipeline approach.

Results The model appears to have learned some aspects of determining the MFE
(Table 2). As a point of reference, the standard deviation of the validation
set is 6.04 kcal/mol. LLMs generally struggle with mathematical tasks [14], so
it is not unexpected that we do not see as large an improvement between the
various approaches as we did in the previous section. With that said,
increasing the amount of training data showed a significant improvement in
accuracy (Fig. 3). Like the previous section, it appears that the combination
of the CoT and model pipeline provides the best result. It is also worth
highlighting that the CoT process results in a lower error than providing the
model with the ground truth secondary structure. This suggests that the
context provided by the nearest neighbor window is not just a means to finding
the secondary structure but is, to some extent, guiding the model to learn the
base pairing/stacking energies.

###  3.3 Sequence design with expert error checking

The design problem, creating DNA sequences that will form a desired secondary
structure, is considerably more difficult than the analysis problems we have
attempted so far. Slight errors in the sequence design can result in self-
complementarity or alignment issues. Once again, we apply a naive, CoT, and
pipeline approach to solving the problem. For the naive approach, we provide
the secondary structure and have the model return a pair of sequences. For
example, Input: “(((((..((((((((((.(+).))))))))))..)))))” Output:
“GCGTTCATGTCTTGCGGGC GGCCGCAAGACACAAACGC”. When applying the CoT approach, we
have the model apply a nearest neighbor window to the secondary structure as
it builds out the sequences. Based on the result from Section 3.1, have the
CoT build out the second sequence as its reverse complement and then on the
final step transform it into its forward sequence. For example, Input:
“..((.(((.(((+))).))).))..” Output: “[_..]:[A,T] [..(]:[AA,TT] [.((]:[AAC,TTC]
[((.]:[AACA,TTCA] [(.(]:[AACAG,TTCAC] [.((]:[AACAGC,TTCACC]
[(((]:[AACAGCC,TTCACCC] [((.]:[AACAGCCG,TTCACCCG] [(.(]:[AACAGCCGG,TTCACCCGC]
[.((]:[AACAGCCGGC,TTCACCCGCC] [(((]:[AACAGCCGGCC,TTCACCCGCCC]
[((_]:[AACAGCCGGCCG,TTCACCCGCCCG] ans:AACAGCCGGCCG CGGGCGGGTGAA”. In the third
condition we have a pipeline where the reverse complement transformation on
the final step is offloaded to a second model or ground truth algorithm.

We now add in an error checking layer into our pipeline of experts (Fig. 1c).
Once our design model produces a sequence pair, we have the expert that we
tuned to predict secondary structures (Section 3.1) to verify that sequences
form the desired structure. If the structures are found to be the same, then
the second strand is transformed into its forward sequence and the final
sequence pair is returned. If the structures are found to be different, then
the design process is repeated again for the same input structure. For
comparison, we also test this approach by having a ground truth error check
where NUPACK performs the sequence analysis in the error checking step.

| naive |  | CoT
---
& rev. comp.
| pipeline
---
CoT
$\rightarrow$ rev. comp. expert
| pipeline
---
CoT
$\rightarrow$ ground truth rev. comp.
accuracy % | 3.9 | 77.6 | 85.9 | 88.9
|  | pipeline
---
CoT
$\rightarrow$ expert error checking
$\rightarrow$ rev. comp. expert
| pipeline
---
CoT
$\rightarrow$ ground truth error checking
$\rightarrow$ rev. comp. expert
accuracy % | 93.1 | 99.8
Table 3: Sequence design accuracy. Figure 4: Sequence design learning curve
for the pipeline with expert error checking approach.

Results In spite of the analysis and design tasks being quite different from
each other, we see similar benefits from the same approaches. With that said,
comparing the results of the first row of approaches in Table 3 to their
analogs in Table 1 confirms that the model has greater difficulty in
performing sequence design. The addition of the error checking layer, however,
appears to compensate for the increase in difficulty. In fact, we see that
with ground truth error checking, the designer can perform almost perfectly.
Based on the steepness of the learning curve, design has more benefit from
larger training sets than analysis does (Fig. 4). For generating this
particular learning curve, we reduced the number of retries per error to 3 as
it would otherwise run for several days for the validation of the low training
sizes to run. The accuracy at the training size of 10,000, is similar between
3 retires and 20 retries. Provided how successful our simple error handling
scheme is, it is also worth considering if error correction may be
implemented. For example, a model that is fine-tuned to reflect on errors and
produce corrections may have even better performance.

##  4 Conclusion

We have shown that a general purpose LLM can be fine-tuned to learn the
structural biophysics of DNA. This is made possible through the combination of
chain-of-thought responses and the chaining of experts. In particular,
breaking down a complicated task into a series of subtasks that models can
master and chaining those models together may be a useful concept for
constructing more powerful models that are capable of working on scientific
problems.

One direction in which this work can be further taken is to test if smaller
models can be chained together for a similar performance improvement. The
implication being that models requiring lower compute resources could
collectively perform more complex tasks than a singular large model. For this
particular type of problem, an LLM architecture involving both an encoder and
decoder may perform better at direct sequence comparison than a decoder-only
architecture.

As noted in the Introduction, our datasets are within a simpler subspace of
the complete range of possible DNA interactions. One may be able to make a
more generalized model by using CoT to search through configurations to deal
with self-complementarity and sequence alignment. We also highlight that the
concepts from this work will also apply to RNA structures. From the
perspective of DNA nanotech, there is a potential opportunity for LLMs to
eventually be useful where NUPACK fails. For example, an LLM may be capable of
learning to predict pseudoknots, Hoogsteen base pairing, and many-strand
interactions (which has utility for designing optimal staple strands for DNA
origami). Further, an LLM trained on experimental data may produce more
accurate structural predictions than the approximations used by current
models.

##  5 Code availability

All code and data used is available at the following link:
https://github.com/TDRoss/DNA-LLM.

## References

  * Karagiorgi et al. [2022] Georgia Karagiorgi, Gregor Kasieczka, Scott Kravitz, Benjamin Nachman, and David Shih.  Machine learning in the search for new fundamental physics.  _Nature Reviews Physics_ , 4(6):399–412, 2022.  doi: 10.1038/s42254-022-00455-1.
  * Jumper et al. [2021] John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Zidek, Anna Potapenko, Alex Bridgland, Clemens Meyer, Simon A. A. Kohl, Andrew J. Ballard, Andrew Cowie, Bernardino Romera-Paredes, Stanislav Nikolov, Rishub Jain, Jonas Adler, Trevor Back, Stig Petersen, David Reiman, Ellen Clancy, Michal Zielinski, Martin Steinegger, Michalina Pacholska, Tamas Berghammer, Sebastian Bodenstein, David Silver, Oriol Vinyals, Andrew W. Senior, Koray Kavukcuoglu, Pushmeet Kohli, and Demis Hassabis.  Highly accurate protein structure prediction with alphafold.  _Nature_ , 596(7873):583+, 2021.  ISSN 0028-0836.  doi: 10.1038/s41586-021-03819-2.
  * Lin et al. [2023] Zeming Lin, Halil Akin, Roshan Rao, Brian Hie, Zhongkai Zhu, Wenting Lu, Nikita Smetanin, Robert Verkuil, Ori Kabeli, Yaniv Shmueli, Allan dos Santos Costa, Maryam Fazel-Zarandi, Tom Sercu, Salvatore Candido, and Alexander Rives.  Evolutionary-scale prediction of atomic-level protein structure with a language model.  _Science_ , 379(6637):1123–1130, 2023.  doi: 10.1126/science.ade2574.
  * Chowdhury et al. [2022] Ratul Chowdhury, Nazim Bouatta, Surojit Biswas, Christina Floristean, Anant Kharkare, Koushik Roye, Charlotte Rochereau, Gustaf Ahdritz, Joanna Zhang, George M. Church, Peter K. Sorger, and Mohammed AlQuraishi.  Single-sequence protein structure prediction using a language model and deep learning.  _Nature Biotechnology_ , 40(11):1617+, 2022.  ISSN 1087-0156.  doi: 10.1038/s41587-022-01432-w.
  * Li et al. [2021] Hong-Liang Li, Yi-He Pang, and Bin Liu.  BioSeq-BLM: a platform for analyzing DNA, RNA and protein sequences based on biological language models.  _Nucleic Acids Research_ , 49(22):e129–e129, 09 2021.  ISSN 0305-1048.  doi: 10.1093/nar/gkab829.
  * Seeman [1982] Nadrian C. Seeman.  Nucleic acid junctions and lattices.  _Journal of Theoretical Biology_ , 99(2):237–247, 1982.  ISSN 0022-5193.  doi: https://doi.org/10.1016/0022-5193(82)90002-9.
  * Rothemund [2006] PWK Rothemund.  Folding dna to create nanoscale shapes and patterns.  _Nature_ , 440(7082):297–302, 2006.  ISSN 0028-0836.  doi: 10.1038/nature04586.
  * Ke et al. [2012] Yonggang Ke, Luvena L. Ong, William M. Shih, and Peng Yin.  Three-dimensional structures self-assembled from dna bricks.  _Science_ , 338(6111):1177–1183, 2012.  doi: 10.1126/science.1227268.
  * Seelig et al. [2006] Georg Seelig, David Soloveichik, David Yu Zhang, and Erik Winfree.  Enzyme-free nucleic acid logic circuits.  _Science_ , 314(5805):1585–1588, 2006.  doi: 10.1126/science.1132493.
  * Zadeh et al. [2011] Joseph N. Zadeh, Conrad D. Steenberg, Justin S. Bois, Brian R. Wolfe, Marshall B. Pierce, Asif R. Khan, Robert M. Dirks, and Niles A. Pierce.  NUPACK: Analysis and design of nucleic acid systems.  _Journal of Computational Chemistry_ , 32(1):170–173, 2011.  doi: https://doi.org/10.1002/jcc.21596.
  * Fornace et al. [2022] Mark E. Fornace, Jining Huang, Cody T. Newman, Nicholas J. Porubsky, Marshall B. Pierce, and Niles A. Pierce.  NUPACK: Analysis and Design of Nucleic Acid Structures, Devices, and Systems.  _ChemRxiv_ , 2022.  doi: 10.26434/chemrxiv-2022-xv98l.
  * Wei et al. [2023] Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, Ed Chi, Quoc Le, and Denny Zhou.  Chain-of-thought prompting elicits reasoning in large language models, 2023.
  * Jacobs et al. [1991] Robert A. Jacobs, Michael I. Jordan, Steven J. Nowlan, and Geoffrey E. Hinton.  Adaptive mixtures of local experts.  _Neural Computation_ , 3(1):79–87, 1991.  ISSN 0899-7667.  doi: 10.1162/neco.1991.3.1.79.
  * Frieder et al. [2024] Simon Frieder, Luca Pinchetti, Ryan-Rhys Griffiths, Tommaso Salvatori, Thomas Lukasiewicz, Philipp Petersen, and Julius Berner.  Mathematical capabilities of chatgpt.  _Advances in Neural Information Processing Systems_ , 36, 2024.


75282

11institutetext:  INAF - Osservatorio Astronomico di Brera, via E. Bianchi 46,
23807 Merate, Italy – 11email<EMAIL_ADDRESS>22institutetext: INAF -
Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, 34131 Trieste,
Italy 33institutetext: IFPU – Institute for Fundamental Physics of the
Universe, Via Beirut 2, 34151 Trieste, Italy 44institutetext: INAF-
Osservatorio Astronomico di Capodimonte, via Moiariello 16, 80131 Napoli,
Italy 55institutetext: Departamento de Fisica - ICEx - UFMG, Belo Horizonte,
MG, Brazil
The remaining affiliations can be found at the end of the paper.

#  CUBES: a UV spectrograph for the future

S. Covino 11 S. Cristiani 2233 J. M. Alcalá 44 S. H. P. Alencar 55 S. A.
Balashev 66 B. Barbuy 77 N. Bastian 8899 U. Battino 1010 L. Bissell 1111 P.
Bristow 1212 A. Calcines 1313 G. Calderone 22 P. Cambianica 1414 R. Carini
1515 B. Carter 1616 S. Cassisi 17171818 B. V. Castilho 1919 G. Cescutti 2020
N. Christlieb 2121 R. Cirami 22 R. Conzelmann 1212 I. Coretti 22 R. Cooke 2222
G. Cremonese 1414 K. Cunha 23232424 G. Cupani 2233 A.R. da Silva 2525 D.
D’Auria 44 V. De Caprio 44 A. De Cia 2626 H. Dekker 2727 V. D’Elia 2828 G. De
Silva 2929 M. Diaz 77 P. Di Marcantonio 22 V. D’Odorico 2233 H. Ernandes 77 C.
Evans 3030 A. Fitzsimmons 3131 M. Franchini 22 B. Gänsicke 3232 M. Genoni 11
R. E. Giribaldi 2525 C. Gneiding 1919 A. Grazian 1414 C. J. Hansen 3333 J.
Hopgood 1212 J. Kosmalski 1212 F. La Forgia 3434 P. La Penna 1212 M. Landoni
11 M. Lazzarin 3434 D. Lunney 1111 W. Maciel 77 W. Marcolino 3535 M.Marconi 44
A. Migliorini 3636 C. Miller 1111 A. Modigliani 1212 P. Noterdaeme 37373838 L.
Oggioni 11 C. Opitom 3939 G. Pariani 11 B. Pilecki 2525 S. Piranomonte 1515 A.
Quirrenbach 2121 E.M.A. Redaelli 11 C. B. Pereira 2323 S. Randich 4040 S.
Rossi 77 R. Sanchez-Janssen 1111 M. Schoeller 1212 W. Seifert 2121 R.
Smiljanic 2525 C. Snodgrass 3939 O. Squalli 1212 I. Stilz 2121 J. Stürmer 2121
A. Trost 222020 E. Vanzella 4141 P. Ventura 1515 O. Verducci 1919 C. Waring
1111 S. Watson 1111 M. Wells 1111 D. Wright 1616 T. Zafar 2929 A. Zanutta 11
G. Zins 1212

(Received: Day Month Year; Accepted: Day Month Year)

###### Abstract

In spite of the advent of extremely large telescopes in the UV/optical/NIR
range, the current generation of 8-10m facilities is likely to remain
competitive at ground-UV wavelengths for the foreseeable future. The
Cassegrain U-Band Efficient Spectrograph (CUBES) has been designed to provide
high-efficiency ($>40$%) observations in the near UV (305-400 nm requirement,
300-420 nm goal) at a spectral resolving power of $R>20,000$, although a
lower-resolution, sky-limited mode of $R\sim 7,000$ is also planned.

CUBES will offer new possibilities in many fields of astrophysics, providing
access to key lines of stellar spectra: a tremendous diversity of iron-peak
and heavy elements, lighter elements (in particular Beryllium) and light-
element molecules (CO, CN, OH), as well as Balmer lines and the Balmer jump
(particularly important for young stellar objects). The UV range is also
critical in extragalactic studies: the circumgalactic medium of distant
galaxies, the contribution of different types of sources to the cosmic UV
background, the measurement of H2 and primordial Deuterium in a regime of
relatively transparent intergalactic medium, and follow-up of explosive
transients.

The CUBES project completed a Phase A conceptual design in June 2021 and has
now entered the Phase B dedicated to detailed design and construction. First
science operations are planned for 2028. In this paper, we briefly describe
the CUBES project development and goals, the main science cases, the
instrument design and the project organization and management.

###### keywords:

Instrumentation: spectrographs – Techniques: spectroscopic

##  1 Introduction

The four 8.2m telescopes of the Very Large Telescope (VLT) at the European
Southern Observatory (ESO) form the world’s most scientifically productive
ground-based observatory in the visible and infrared. However, looking at the
future of the VLT, there is a long-standing need for an optimised ultraviolet
(UV) spectrograph (Barbuy et al., 2014) with a large increase of efficiency
with respect to existing instruments (UVES and X-Shooter).

The European Extremely Large Telescope (ELT), under construction in northern
Chile by ESO, with a primary aperture of 39m will be unprecedented in its
light-gathering power, coupled with exquisite angular resolution via
correction for atmospheric turbulence by adaptive optics (AO). At variance
with current large telescopes such as the VLT, AO is an integral part of the
ELT, which has a five-mirror design including a large adaptive mirror (M4) and
a fast tip-tilt mirror (M5). The choice of protected silver (Ag+Al) for the
ELT mirror coatings (apart from M4) ensures a durable, proven surface with
excellent performance across a wide wavelength range. However, the performance
drops significantly in the blue-UV part of the spectrum compared to bare
aluminium. ESO is actively researching alternative coatings, but in the short-
medium term we can assume that the performance of the ELT in the blue-UV will
be limited. Indeed, during the Phase A study of the MOSAIC multi-object
spectrograph (Evans et al., 2016) it was concluded that a blue-optimised
instrument on the VLT could potentially be competitive with the ELT at
wavelengths shorter than 400 nm (Fig. 1). In addition, this spectral range is
complementary to the ELT and JWST. Motivated by this, in 2018 we revisited
(Evans et al., 2018) the Phase A study undertaken in 2012 of the Cassegrain
U-band Brazilian-ESO Spectrograph. The past study investigated a $R\sim 20$k
spectrograph operating at ‘ground UV’ wavelengths (spanning 300-400 nm) to
open-up exciting new scientific opportunities compared to the (then) planned
instrumentation suite for Paranal Observatory (Barbuy et al., 2014; Bristow et
al., 2014).

Figure 1: Comparison of the total (instrument+telescope+sky) CUBES efficiency
in the $R>20$ K mode with respect to UVES.

In January 2020 ESO issued a Call for Proposal for a Phase A study of a UV
Spectrograph to be installed at a Cassegrain focus of the VLT, with the goal
of high-efficiency ($>40$%) and intermediate resolving power ($\sim$ 20K) in
the ground-UV domain (305-400 nm requirement, 300-420 nm goal). In May 2020
the CUBES (Cassegrain U-Band Efficient Spectrograph) Consortium, led by
INAF111Istituto Nazionale di AstroFisica, was selected to carry out the study.
The CUBES project completed a Phase A conceptual design study in June 2021.
After the endorsement by the ESO Council at the end of 2021, Phase B started
in February 2022 with the signature of the Construction Agreement between ESO
and the leading institute of the CUBES Consortium, opening the detailed design
and construction phase. Here we report the present status of the project,
which will provide a world-leading UV capability for ESO from 2028 well into
the ELT era. More detailed information about the project is reported in
Cristiani et al. (2022).

##  2 Science with CUBES

The CUBES science case covers a wide range of astrophysical topics. We propose
below a brief highlight of the main key cases across the Solar System,
Galactic, and extra-galactic fields (see also Evans et al., 2022).

###  2.1 Searching for water in the asteroid belt

The search for water in our solar system is a long-standing problem (Opitom et
al., 2022). It is a difficult task with ground-based facilities, given the
water content of Earth’s atmosphere. The typical diagnostics of water
outgassing from small bodies is the OH emission at 308 nm. Observation of the
OH line has been possible so far for a few active comets while they are near
the Sun and Earth, with severe limitations. We still miss knowledge of water
production around their orbits and the role of seasonal effects that the
Rosetta mission revealed to be important. In general, most comets are simply
too faint to be studied with current facilities. Main-belt comets, bodies in
asteroidal orbits, can undergo activity thought to arise from sublimation.
Constraining the OH emission of these objects is well beyond our current
capabilities. Since main-belt comets show a size distribution similar to the
general population in the asteroid belt, the detection of outgassing water
with CUBES would point to a potentially large population of icy bodies. This
could imply a large reservoir of water, a parameter of considerable interest
in models of the formation and evolution of the inner solar system.

###  2.2 Accretion, winds & outflows in YSOs

The evolution of circumstellar disks, mass accretion around young stars, and
outflow and winds are fundamental aspects of the formation of protoplanets.
Observations about these phenomena require multi-wavelengths studies of stars
during the first 10 Myr of their evolution and in particular of Classical T
Tauri stars (CTTS). These young, low- to solar-mass stars are actively
accreting mass from planet-forming disks. Spectroscopic surveys of CTTS in
nearby star-forming regions have been carried out to study the often complex
relationships between accretion, jets and disk structure. CUBES, both due to
its increased UV sensitivity and coverage of a critical wavelength range, will
enable more detailed studies of the accretion processes/wind-outflows than
currently possible as well as studies of CCTS in star-forming region at larger
distances.

###  2.3 Bulk composition of exo-planets

In the past few decades, we have learned that it is normal for stars to have
planets and the study of exoplanet formation and evolution has become a major
astrophysical topic. The best approach available at present for estimating the
bulk composition of exo-planet systems is based on spectroscopic analysis of
evolved white dwarf (WD) stars accreting debris from tidally-disrupted
planetesimals. WDs are hot so most of their abundance diagnostics are in the
near-UV (e.g. Sc, Ti, V, Cr, Mn, Fe, Ni). However, WDs are also intrinsically
faint, and only about twenty systems have precise abundances so far. CUBES
will transform this exciting area of exo-planet research by increasing the
sample of known exo-planetesimal compositions providing precise constraints on
the next generation of planet-formation models.

###  2.4 Stellar nucleosynthesis

The spectral features of more than a quarter of the chemical elements are only
observable in the near UV, but the low efficiency of instruments in this
domain severely restricted previous studies. Advancements in the field require
high-resolution, near-UV spectroscopy of a large number and diversity of
stars. Three main CUBES science cases deal with this topic:

i) Metal-poor stars and light elements. A key case is to probe the early
chemical evolution of the Galaxy, via chemical abundance patterns in the
oldest, low-mass stars that formed from material enriched by the first
supernovae. The so-called Carbon-enhanced metal-poor (CEMP) stars are the
perfect probes to investigate nucleosynthesis by the first stars. CUBES will
enable quantitative spectroscopy for large samples of metal-poor stars,
providing direct estimates for a broad range of heavy elements, as well as
valuable constraints on CNO elements.

ii) Heavy-element nucleosynthesis. Stellar abundances from CUBES will provide
critical tests of the various production channels of heavy elements for both
r- and s-process elements. Determining the abundances of neutron-capture
elements in metal-poor stars is fundamental to understand the physics of these
processes and the chemical evolution of the Galaxy as well as the origin of
the Galactic halo. Since lines due to many of these elements are in the UV
domain (e.g. Hf, Sn, Ag, Bi) and have only been measured for a very restricted
number of stars, CUBES will play a critical role to fill this gap.

iii) Beryllium is one of the lightest and simplest elements. Nevertheless,
questions remain about its production in the early Universe. Recent results
are consistent with no primordial production, but larger samples are required
to investigate this further. Only $\sim 200$ stars have Be abundances so far
(limited to $V$ $\sim$ 12 mag in a few hrs with UVES, Dekker et al., 2000).
CUBES will provide large homogeneous samples of Be abundances in stars
belonging to different populations up to three magnitudes deeper, providing
new insights into its production and tracing the star-formation history of the
Galaxy (see Fig. 2).

Figure 2: Results of fitting four simulated observations of a bright (V = 12.5
mag) subgiant star (Teff = 5600 K and $\log$ g = 3.4 dex) with [Fe/H] = -3.5
and $\log$(Be H) = -13.5. The final simulated observations have different
realizations of SNR = 340 and were computed to have R = 23 K and sampling of
2.35 px. Top Left: One of the best fit synthetic spectra is shown in the plot
and has the same Be abundance of the simulated observation. Top Right: The
best fit is chosen using the coefficient of determination, $R^{2}$, which
involves the ratio between the residual sum of squares and the total sum of
squares. Bottom: The boxplot displays the best fitting Be abundances for each
one of the four simulated observations (with results deviating at most by 0.05
dex from the input Be abundance).

###  2.5 Primordial deuterium abundance

Within the Standard Model of particle physics and cosmology there is still no
accepted model for dark energy and dark matter, or why the Universe contains
baryons instead of antibaryons, or even why the Universe contains baryons at
all. We are also missing crucial properties of neutrinos (e.g. their
hierarchy, why they change flavour, and the number that existed during the
earliest phases of the Universe). Some of these questions can be investigated
by measuring the nuclides produced a few minutes after the Big Bang. The
primordial deuterium (D/H) abundance is currently our most reliable probe of
Big Bang Nucleosynthesis (Cooke et al., 2014). CUBES will provide a large,
reliable sample of D/H estimates from quasar absorption spectra. Its
significant gain at the shortest wavelengths compared to existing facilities
will enable observations at lower redshifts (less contamination by the Lyman-
alpha forest) giving more absorption-line systems from which to estimate D/H
and smaller uncertainties.

###  2.6 The missing baryonic mass at the cosmic noon

Remarkable progresses about the missing baryon problem has been recently made
possible at low redshifts by studying the dispersion measure in Fast Radio
Bursts (FRBs) (Macquart et al., 2020) and at $z>1.5$ by observations and
simulations of the Lyman forest (e.g., Weinberg et al., 1997). Still, we have
insufficient knowledge about how baryonic matter is distributed among the
different gaseous components and we would need to better constrain the
mechanisms (stellar and AGN feedback, accretion, etc.) that determine the
observed distribution. A UV efficient spectrograph with relatively high
resolution offers the possibility to dig into the complex nature of the inter-
and circum-galactic gas at $z\sim$ 1.5 to 3, via two experiments with quasar
absorption lines: i) The baryons in the diffuse IGM are studied through the
detection and analysis of Lyman-$\alpha$ lines at $z\simeq 1.5$ to 2.3. This
redshift range, immediately after the era of peak star-formation in the
Universe, is poorly investigated due to observational difficulties as the low
efficiency of ground-based spectrographs in the UV, but is critical to connect
the low- and high-redshift results. ii) Observing the O VI absorption lines at
$1.9<z<2.9$ to trace the warm-hot gas at $T>10^{5}$ K, associated with the IGM
or with the CGM (Lehner et al., 2014). In all cases spectroscopy in the
wavelength range at $\lambda>400$ nm is necessary to complement the
information on the neutral IGM component derived from the Lyman forest,
checking the associated metal absorption lines (in particular due to C IV and
Si IV) and deriving the contribution of the ionised gas. It is also needed to
complete the coverage of the associated HI and metal transitions. To this aim
spectra of the same targets obtained at higher resolution with, e.g., UVES/VLT
(simultaneously via a fiber link or retrieved from the archives) will be
needed.

###  2.7 Cosmic UV background

Galaxies are likely able to produce most of the UV emissivity needed for
cosmic reionisation at high redshift but quasars also possibly contribute.
Estimates of the escape fraction (fesc) of hydrogen-ionising photons able to
escape a galaxy are close to 100% for quasars. However, the volume density of
low- and intermediate-luminosity quasars at $z$ $>$ 4 is still uncertain, so
it is unclear if they are the dominant source of ionisation. In contrast,
star-forming galaxies are more numerous, but estimates of fesc from
observations of the Lyman continuum ($\lambda_{\rm rest}$ $<$ 91.2 nm) have
uncertainties of tens of percent and are limited to a handful of systems at
$z$ = 2.5 to 4. To be detectable from Earth escaping photons have to survive
absorption along the line of sight by the intergalactic medium, which become
stronger with redshift and is significantly variable between sightlines. Given
these competing factors, the ideal redshift range for ground-based
observations of the Lyman continuum of a galaxy is $z$ = 2.4 to 3.5, i.e. from
about 410 nm down to the atmospheric cut-off. For this reason CUBES could be
an asset for this science case thanks to its high throughput. Furthermore,
since the galaxies to be observed are extremely faint this science case is
also one of the main drivers of the low resolution mode.

###  2.8 Transient astronomy

Time-domain astronomy is one of the most active branches of modern
astrophysics. In a few years, new observational facilities, specifically
designed with the goal of securing high-cadence observations of large
fractions of the nightly sky, will become operational. Equally important,
“big-data” algorithms are increasingly being applied and developed to manage
the large amount of data provided by these facilities. The discovery space
opened by rare or peculiar transients is very large, involving all categories
of sources. For low or high redshift objects, a highly efficient UV
spectrograph can shed light on a variety of physical ingredients and, in this
context, the possible synergy of the CUBES and UVES spectrographs could open
the exciting perspective of a UV-blue continuous spectral coverage.

##  3 From Science to Requirements

The science cases of interest for the CUBES community defined the reference
for the development of the Top level Requirements (TLR):

  * •

Spectral range: CUBES must provide a spectrum of the target over the entire
wavelength range of 305 – 400 nm in a single exposure (goal: 300 – 420 nm).

  * •

Eﬃciency: The eﬃciency of the spectrograph, from slit to detector (included),
has to be $>40$% for 305 – 360 nm (goal $>45$%, with $>50$% at 313 nm), and
$>37$% (goal $40$%) between 360 and 400 nm.

  * •

Resolving power ($R$): In any part of the spectrum, $R$ needs to be $>19$ K,
with an average value $>20K$.

  * •

Signal-to-noise (S/N) ratio: In a 1 hr exposure the spectrograph must be able
to obtain, for an A0-type star of $U$ = 17.5 mag (goal $U\geq 18$ mag), a S/N
= 20 at 313 nm for a 0.007 nm wavelength pixel.

During Phase A studies an important addition was identified with the provision
of a second (lower) resolving power (with $R\sim 7$k), to enable background-
limited observations of faint sources where spectral resolution is less
critical. There are also studies for a fiber link to UVES, in order to provide
simultaneous observations at longer wavelengths. This would considerably
broaden the scientific capabilities of the project.

##  4 Instrument Design Overview

The instrument is designed to be used alone or combined with the fiber-feed to
UVES. Two resolution modes (HR, $R>20$ K; LR $R\sim 7$ K) are enable by the
exchange of two independent image slicers. An Active Flexure Compensation
system (AFC) is part of the baseline. All the top level requirements (TLRs),
in particular those related to efficiency, are met (see Fig. 3 for a view of
the whole instrument).

Figure 3: Functional design of CUBES. Light path is from the top to the
bottom. The shown acronyms are: FL cam (fibre-link A&G camera), ND filters
(Neutral Density filters), WL filter (Wavelength filter), ADC (Atmospheric
Dispersion Corrector), P (single Pin-hole mask), Ps (multi pin-holes mask),
A&G (Acquisition and Guiding), Cal mirror (Calibration mirror), DC (Dichroic),
AFC (Active Flexure Compensation), LR (Low Resolution), HR (High Resolution),
Cryo (Cryocooler), FF LED (Flat-Field LED).

###  4.1 Instrument sub-systems and Operations

The current baseline design of CUBES includes a calibration unit that provides
the light sources necessary to register frames for ﬂat ﬁelding, wavelength
calibration, alignment, and the AFC. A foreoptics sub-system includes an
atmospheric dispersion corrector (ADC) and Acquisition and Guiding
functionalities. There are two user-selectable image slicers (to enable
different spectral resolutions) followed by a dichroic beamsplitter that feeds
two spectrograph arms, each consisting of a Fused Silica single-lens
collimator, a first-order transmission grating with a groove density up to
3600 l/mm, and a 3-lens all-silica camera. Each arm has its own detector
cryostat, with a 9k or 10k CCD detector (we also have an option to increase
the sampling by 11% using the STA 10k 9$\mu m$ detector instead of the E2V 9K
10$\mu m$), read-out electronics, cryo-vacuum components (both hardware and
specific control electronics). The Instrument Control Electronics are based on
PLCs that are compliant with latest ELT design standard, and control all
optomechanical and cryo/vacuum functions. The Scientific Detector system is
controlled by ESOs new NGC2 standard. The Instrument Software package has
elaborate instrument control software, data-reduction and simulation tools
(see Sect.4.4) for details). And, finally, a Fiber Link unit provides the
option of simultaneous observations with UVES by injecting red light into
optical fibers (1 object, 3 sky) that subtend 1 arcsec on the sky and are
approximatively 40 m long to UVES on the Nasmyth platform (Dekker et al.,
2000).

###  4.2 Optics and Dispersing Elements

Using two lens doublets and a number of folding prisms the foreoptics relays a
FoV of 6”x10” for LR and 1.5”x10” for HR at the telescope focus to the
entrance plane of the spectrograph. Zero-deviation ADC prisms in the parallel
beam between the doublets provide atmospheric dispersion correction over a
range 300-405 nm for zenith angles of 0-60∘. By inserting a dichroic just
below the telescope focal plane, light redward of 420 nm may be directed to
the UVES fiber feed. At the magnified telescope focal plane produced by the
fore-optics (0.5 arcsec/mm plate scale), two user-selectable reflective image
slicers are used to reformat the field of view. The first component, an array
of six spherical slicer mirrors decomposes the rectangular FoV into six slices
which are reimaged by six spherical camera mirrors composing the spectrograph
entrance slit, defined by a slit mask. The slicer efficiency is expected to be
$>90\%$ (goal 94%) The output slit mask has six slitlets, corresponding to six
slices, each one measuring 0.25”x10” on the sky for the HR slicer ($R\sim
20K$) and 1”x10” for the LR slicer ($R\sim 7K$). Further slit mask apertures
are illuminated by a ThAr fiber source for use by the AFC system.

The light coming from the slit mask is folded by a Total Internal Reflection
(TIR) prism and then reaches a dichroic which splits the light by reflecting
the Blue-Arm passband (300–352.3 nm) and transmitting the Red-Arm passband
(346.3–405 nm).

In order to achieve a high ($>20K$) resolution without the efficiency losses
associated with cross-dispersed echelles, CUBES uses state-of-the-art first-
order dispersing elements. Binary transmission gratings produced by E-beam
microlithography and an Atomic Layer Deposition (ALD) overcoat have been
identified as a suitable technology (see Zeitner et al., 2022). Their
theoretical average (RCWA) diffraction efficiency is $>90\%$ and studies
carried out through simulations and prototyping show that the measured
efficiency is compliant with the expectation and demonstrate the feasibility
of the instrument in terms of light throughput.

###  4.3 Mechanics

To achieve high resolution, CUBES requires a fairly large beam diameter of 160
mm and a collimator focal length of 3 m. In order to limit the total mass, a
light-weight construction principle has been adopted. The optical layout
contains several folds so all optical elements. The optical layout was
optimized such that all optical elements of the spectrograph from slit to
detector lie in a single plane, so all spectrograph optics can be mounted on a
single optical bench. This is arguably the most stable configuration since the
dispersion direction of CUBES is parallel to the stiff surface plane of the
optical bench. A general focus of the mechanical design is, in fact, to
minimize the effects of gravitational bending of the instrument.

In the current design, the CUBES main mechanical structure is divided into
three main components: 1. A telescope adapter, that provides a stiff
connection between the Cassegrain telescope flange and the optical bench
assembly; 2. An optical bench that provides a stable platform for the
spectrograph optics as well as for the foreoptics; 3. An assembly to provide
support for auxiliary equipment such as electronic racks, the calibration unit
and vacuum equipment. In Fig. 4 the mechanical concept of CUBES is shown.

Figure 4: Mechanical concept for CUBES: The general layout of the main
mechanical components is shown. For reference, the Telescope Adapter has a
diameter of about 1.5 m. The Fore-Optics Assembly is located near the center
of the bench, while the spectrograph opto-mechanics are ‘hanging’ on the
bottom side of the same bench.

###  4.4 Software

The CUBES instrument is designed including a “software ecosystem”, whose
individual packages cooperate to support the users from the proposal
preparation to the science-grade spectra: i) the Exposure Time Calculator
(ETC), a web application used to predict the CUBES exposure time required to
achieve a given SNR; ii) the Observation Preparation Software (OPS): a list of
tools aimed to help the users identify the best instrument settings to achieve
a scientific goal; iii) the Instrument Control Software (ICS) and the Detector
Control Software (DCS): devoted to the instrument devices and detectors
control; iv) the Data Reduction Software (DRS): a collection of recipes aimed
to remove instrument signature from the science exposures, and produce the
final calibrated 2D and 1D spectra; v) the End-to-end Simulator (E2E): a
package able to simulate realistic science exposures of a given science
target, by taking into account the CUBES instrumental effects, and allowing
early testing of the data reduction pipelines, as well as early validation of
design decisions.

The above mentioned packages are developed according to the recently published
ELT software standards, and will be based on the ELT Instrument Framework
libraries and tools.

##  5 Project and Management

The CUBES consortium is composed of institutes from five countries:

  * •

INAF - Istituto Nazionale di Astrofisica, Italy, (consortium leader)

  * •

IAG-USP - Instituto de Astronomia, Geofísica e Ciências Atmosféricas (primary
Brazil partner) and LNA - Laboratório Nacional de Astrofísica (secondary
Brazil partner), Brazil

  * •

LSW - Landessternwarte, Zentrum für Astronomie der Universtität Heidelberg,
Germany

  * •

NCAC - Nicolaus Copernicus Astronomical Center of the Polish Academy of
Sciences, Poland

  * •

STFC-UKATC - UK Astronomy Technology Centre, (primary UK partner) and Durham
University Centre for Advanced Instrumentation (secondary UK partner), United
Kingdom

The Consortium organization is fairly standard, with a Principal Investigator
(PI) with the ultimate responsibility for the project, acting as the formal
contact point between ESO and the Consortium. The PI represents the leading
technical institute, INAF. Each country is then represented in the managerial
structure by one Co-PI; together they form the CUBES Executive Board (EB). The
managerial aspects are delegated by the EB to the Project Manager (PM). The
scientific aspects are delegated by the EB to the Project Scientist (PS). The
project manager is supported by a System Engineer (SE) and by a Software
System Engineer (SSE) who are in charge to supervise the overall system
design. The SE and SSE work in close contact with the Instrument Scientist
(IS) who makes sure that the adopted technical solutions match the foreseen
instrument scientific needs.

CUBES follows the standard project phasing for ESO instruments which is based
on the stage-gate paradigm. Important decision points are project milestones
(gates of the project) which mark the transition into a new stage when
successfully completed. In the current plan CUBES will be available to the ESO
user community in 2028.

###  5.1 Public Engagement

CUBES is an ambitious research program, and some of the scientific topics are
related to the hottest open questions in modern astrophysics. Considering the
vast discovery potential of the project, and the remarkable research and
development technological activities, we consider good public communication as
particularly important. Dissemination of science and technology is a
fundamental part of our project. We have prepared a web page that is also a
useful tool for the project as a whole222https://cubes.inaf.it/home, and
profiles in the main social media, i.e. Facebook, Twitter etc.

##  6 Conclusions

The Cassegrain U-Band Efficient Spectrograph (CUBES) for the ESO VLT has been
presented. Analysis of the design shows that it will deliver outstanding
($>40$%) throughput across its bandpass, at a mean $R>20$ K (HR mode) and
$R\sim 7K$ (LR mode). A fiber link from CUBES to UVES is being studied, which
would provide the capability of simultaneous high-resolution spectroscopy at
$\lambda>420$ nm. The CUBES design is able to address a large variety of
scientific cases, from Solar System science to Cosmology, with no obvious
technical showstopper. With contributions from institutes in five countries,
the CUBES design is well placed to become the most efficient ground-based
spectrograph at near-UV wavelengths, with science operations anticipated for
2028, opening a unique discovery space for the VLT for years to come.

Affiliations

6Ioffe Institute, HSE University, Saint-Petersburg, Russia

7Universidade de São Paulo, IAG, Rua do Matão 1226, São Paulo, Brazil

8Donostia International Physics Center (DIPC), Guipuzkoa, Spain

9IKERBASQUE Basque Foundation for Science, Bilbao, Spain

10University of Hull, E.A. Milne Centre for Astrophysics, Hull, UK

11STFC - United Kingdom Astronomy Technology Centre (UK ATC), Edinburgh, UK

12European Southern Observatory (ESO), ESO Headquarters Karl-Schwarzschild-
Str. 2 85748 Garching bei München Germany

13Durham University, Department of Physics, Centre for Advanced
Instrumentation, Durham, UK

14INAF - Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 3,
Padova, Italy

15INAF - Osservatorio Astronomico di Roma, Via Frascati 33, Monte Porzio
Catone, Italy

16Centre for Astrophysics, University of Southern Queensland, Toowoomba 4350,
Australia

17INAF - Osservatorio Astronomico di Abruzzo, Via M. Maggini, I-64100 Teramo,
Italy

18INFN - Sezione di Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy

19LNA/MCTI, Laboratorio Nacional De Astrofisica, Itajubá, Brazil

20Dipartimento di Fisica, Sezione di Astronomia, Università di Trieste, Italy

21Landessternwarte, Zentrum für Astronomie der Universität Heidelberg,
Heidelberg, Germany

22Centre for Extragalactic Astronomy, Durham University, Durham DH1 3LE, UK

23Observatório Nacional, Rua Gen. José Cristino 77, São Cristóvão, Rio de
Janeiro, Brazil

24Steward Observatory, University of Arizona, 950 N. Cherry Ave., Tucson, AZ,
85719

25Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw,
Poland

26Department of Astronomy, University of Geneva, Chemin Pegasi 51, Versoix,
Switzerland

27Consultant Astronomical Instrumentation, Alpenrosenstr.15, 85521 Ottobrunn,
Germany

28Italian Space Agency - Space Science Data Centre, via del Politecnico snc,
Rome, Italy

29Australian Astronomical Optics, Macquarie University, North Ryde, NSW 2113,
Australia

30European Space Agency (ESA), ESA Office, Space Telescope Science Institute,
3700 San Martin Drive, Baltimore, MD 21218, USA

31Astrophysics Research Centre, Queen’s University, Belfast, UK

32University of Warwick, Department of Physics, Gibbet Hill Road, Coventry,
CV7 4AL, UK

33Goethe University Frankfurt, Institute for Applied Physics, Frankfurt am
Main, Germany

34Dipartimento di Fisica e Astronomia dell’Università, Vicolo
dell’Osservatorio 3, Padova, Italy

35Observatório do Valongo, Universidade Federal do Rio de Janeiro, Brazil

36INAF - Institute of Space Astrophysics and Planetology, Roma, Italy

37Franco-Chilean Laboratory for Astronomy, Las Condes, Santiago, Chile

38Institut d’Astrophysique de Paris, CNRS-SU, UMR 7095, 98bis bd Arago, Paris,
France

39Institute for Astronomy, University of Edinburgh, Royal Observatory,
Edinburgh, UK

40INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125,
Firenze, Italy

41INAF - Osservatorio di Astrofisica e Scienza dello Spazio, Bologna, Italy

###### Acknowledgements.

R.S. acknowledges support by the Polish National Science Centre through
project 2018/31/B/ST9/01469. We gratefully acknowledge support from the German
Federal Ministry of Education and Research (BMBF) through project 05A20VHA.
B.B. acknowledges the FAPESP grant 2014/18100-4. For the purpose of open
access, the author has applied a Creative Commons Attribution (CC BY) licence
to any Author Accepted Manuscript version arising from this submission.

## References

  * Barbuy et al. (2014) Barbuy, B., Bawden Macanhan, V., Bristow, P., et al. 2014, Ap&SS, 354, 191
  * Bristow et al. (2014) Bristow, P., Barbuy, B., Macanhan, V. B., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9147, Ground-based and Airborne Instrumentation for Astronomy V, ed. S. K. Ramsay, I. S. McLean, & H. Takami, 914709
  * Cooke et al. (2014) Cooke, R. J., Pettini, M., Jorgenson, R. A., Murphy, M. T., & Steidel, C. C. 2014, ApJ, 781, 31
  * Cristiani et al. (2022) Cristiani, S., Alcalá, J. M., Alencar, S. H. P., et al. 2022, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 12184, Ground-based and Airborne Instrumentation for Astronomy IX, ed. C. J. Evans, J. J. Bryant, & K. Motohara, 121840A
  * Dekker et al. (2000) Dekker, H., D’Odorico, S., Kaufer, A., Delabre, B., & Kotzlowski, H. 2000, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 4008, Optical and IR Telescope Instrumentation and Detectors, ed. M. Iye & A. F. Moorwood, 534–545
  * Evans et al. (2022) Evans, C., Cristiani, S., Opitom, C., et al. 2022, Experimental Astronomy
  * Evans et al. (2018) Evans, C. J., Barbuy, B., Castilho, B., et al. 2018, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 10702, Ground-based and Airborne Instrumentation for Astronomy VII, ed. C. J. Evans, L. Simard, & H. Takami, 107022E
  * Evans et al. (2016) Evans, C. J., Puech, M., Rodrigues, M., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, ed. C. J. Evans, L. Simard, & H. Takami, 99089J
  * Lehner et al. (2014) Lehner, N., O’Meara, J. M., Fox, A. J., et al. 2014, ApJ, 788, 119
  * Macquart et al. (2020) Macquart, J. P., Prochaska, J. X., McQuinn, M., et al. 2020, Nature, 581, 391
  * Opitom et al. (2022) Opitom, C., Snodgrass, C., Forgia, F. L., et al. 2022, Experimental Astronomy
  * Weinberg et al. (1997) Weinberg, D. H., Miralda-Escudé, J., Hernquist, L., & Katz, N. 1997, ApJ, 490, 564
  * Zeitner et al. (2022) Zeitner, U. D., Dekker, H., Burmeister, F., et al. 2022, Experimental Astronomy