meta-information of the Document    {'Published': '2016-05-26',     'Title': 'Heat-bath random walks with Markov bases',     'Authors': 'Caprice Stanley, Tobias Windisch',     'Summary': 'Graphs on lattice points are studied whose edges come from a finite set of\nallowed moves of arbitrary length. We show that the diameter of these graphs on\nfibers of a fixed integer matrix can be bounded from above by a constant. We\nthen study the mixing behaviour of heat-bath random walks on these graphs. We\nalso state explicit conditions on the set of moves so that the heat-bath random\nwalk, a generalization of the Glauber dynamics, is an expander in fixed\ndimension.'}docs[0].page_content[:400]  # a content of the Document    'arXiv:1605.08386v1  [math.CO]  26 May 2016\nHEAT-BATH RANDOM WALKS WITH MARKOV BASES\nCAPRICE STANLEY AND TOBIAS WINDISCH\nAbstract. Graphs on lattice points are studied whose edges come from a Ô¨Ånite set of\nallowed moves of arbitrary length. We show that the diameter of these graphs on Ô¨Åbers of a\nÔ¨Åxed integer matrix can be bounded from above by a constant. We then study the mixing\nbehaviour of heat-b'Question Answering on facts‚Äã# get a token: https://platform.openai.com/account/api-keysfrom getpass import getpassOPENAI_API_KEY = getpass()     ¬∑¬∑¬∑¬∑¬∑¬∑¬∑¬∑import osos.environ["OPENAI_API_KEY"] = OPENAI_API_KEYfrom langchain.chat_models import ChatOpenAIfrom langchain.chains import ConversationalRetrievalChainmodel = ChatOpenAI(model_name="gpt-3.5-turbo")  # switch to 'gpt-4'qa = ConversationalRetrievalChain.from_llm(model, retriever=retriever)questions = [    "What are Heat-bath random walks with Markov base?",    "What is the ImageBind model?",    "How does Compositional Reasoning with Large Language Models works?",]chat_history = []for question in questions:    result = qa({"question": question, "chat_history": chat_history})    chat_history.append((question, result["answer"]))    print(f"-> **Question**: {question} \n")
arXiv is an open-access archive for 2 million scholarly articles in the fields of physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics.
arXiv is an open-access archive for 2 million scholarly articles in the fields of physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics. ->: meta-information of the Document    {'Published': '2016-05-26',     'Title': 'Heat-bath random walks with Markov bases',     'Authors': 'Caprice Stanley, Tobias Windisch',     'Summary': 'Graphs on lattice points are studied whose edges come from a finite set of\nallowed moves of arbitrary length. We show that the diameter of these graphs on\nfibers of a fixed integer matrix can be bounded from above by a constant. We\nthen study the mixing behaviour of heat-bath random walks on these graphs. We\nalso state explicit conditions on the set of moves so that the heat-bath random\nwalk, a generalization of the Glauber dynamics, is an expander in fixed\ndimension.'}docs[0].page_content[:400]  # a content of the Document    'arXiv:1605.08386v1  [math.CO]  26 May 2016\nHEAT-BATH RANDOM WALKS WITH MARKOV BASES\nCAPRICE STANLEY AND TOBIAS WINDISCH\nAbstract. Graphs on lattice points are studied whose edges come from a Ô¨Ånite set of\nallowed moves of arbitrary length. We show that the diameter of these graphs on Ô¨Åbers of a\nÔ¨Åxed integer matrix can be bounded from above by a constant. We then study the mixing\nbehaviour of heat-b'Question Answering on facts‚Äã# get a token: https://platform.openai.com/account/api-keysfrom getpass import getpassOPENAI_API_KEY = getpass()     ¬∑¬∑¬∑¬∑¬∑¬∑¬∑¬∑import osos.environ["OPENAI_API_KEY"] = OPENAI_API_KEYfrom langchain.chat_models import ChatOpenAIfrom langchain.chains import ConversationalRetrievalChainmodel = ChatOpenAI(model_name="gpt-3.5-turbo")  # switch to 'gpt-4'qa = ConversationalRetrievalChain.from_llm(model, retriever=retriever)questions = [    "What are Heat-bath random walks with Markov base?",    "What is the ImageBind model?",    "How does Compositional Reasoning with Large Language Models works?",]chat_history = []for question in questions:    result = qa({"question": question, "chat_history": chat_history})    chat_history.append((question, result["answer"]))    print(f"-> **Question**: {question} \n")