Monday, 30 October 2023

Couvreur 95 - Couverture Mayer Charles

 


Demoussage Toiture avec Couvreur Deuil-la-Barre 95170 demoussage toiture deuil-la-barre 95170 En Île de France, le climat et la pollution tout au long de l'année fragilise la toiture de votre habitation si vous n'en prenez pas soin. Changements de température, les vents, l'humidité, les pluies etc font apparaitre sur votre toiture des salissures, des algues, des mousses, des champignons. Il faut un entretien de toiture régulier pour protéger votre habitation. Ne laissez pas les tuiles de votre toiture se fragiliser et devenir de plus en plus poreuse, jusqu'à se briser, se déplacer et faire apparaître des fuites qui peuvent vite faire monter la facture.

Couvreur à Deuil-la-Barre vient sur place vous faire un diagnostique gratuit ainsi qu'un devis sur mesure pour vous faire un travail de qualité.

Nettoyage haute pression de votre toiture après vérification de l'état de celle-ci demoussage toiture avec des produits professionels de qualité et reconnus anti mousse pro pour toiture sans ( javel ou autres acides ) traitement hydrofuge sur toutes toitures après après vérification de l'état de celle-ci Tous types de Peintures de toits après vérification de l'état de celle-ci et les besoin du client Vérification des tuiles et gouttières en cas de fuites ou autres travaux à prévoir Réparation toiture ( tuiles, zinc, etc )

Vous allez retrouvez une toiture avec une seconde jeunesse pour de longues années après le travail de qualité fait par notre service spécialiste des couvertures - toitures -toits. Faire Appel à Couvreur Deuil-la-Barre 95170 est un gage de Qualité et satisfaction pour votre projet. Nous sommes à votre disposition pour tous renseignement Contactez-nous au 06.41.04.91.79

 

Sunday, 29 October 2023

Muki Venture TTvSA

 


Walk,Hike,Bike Table Mountain & Lions Head
Table Mountain, with its striking silhouette and panoramic views of Cape Town, is more than just a geological wonder; It is a place of tranquility and natural beauty that captures the hearts of locals and tourists alike.

To truly immerse yourself in the essence of this iconic landmark, embark on a guided tour with Muki Venture, an accredited tour guide who will provide you with an unforgettable experience as you watch the sun rise or set gracefully over the breathtaking scenery of Table Mountain .

Cape Town, the vibrant capital city of South Africa, is renowned for its stunning beaches, cosmopolitan flair, and iconic landmarks such as Table Mountain and the Cape of Good Hope.

But beyond its bustling urban center lies a hidden treasure waiting to be explored – the diverse and breathtaking nature trails of Cape Town.

Thursday, 19 October 2023

Muki Venture TTvSA


 https://instagram.com/mukiventure_ttvsa?igshid=YTQwZjQ0NmI0OA%3D%3D&utm_source=qr



https://www.tiktok.com/@mukiventure_ttvsa?_t=8gaFIR0rYxy&_r=1

https://www.mukiventure.co.za

Hike Table Mountain or Lions Head with an accredited guide.

The ultimate one-stop platform for finding the most unique, activities in Cape Town and South Africa. We offer a wide range of experiences, from hiking Table Mountain to Mountain Biking.

We make it easy to explore the best of what Cape Town has to offer.

Austria, China, France, Germany, Ireland, Israel, Italy, Japan, Luxembourg, Netherlands, New Zealand, Norway, South Africa, Spain, United Arab Emirates, Ukraine, United Kingdom and United States, Belgium, Norway, South Aftica, Switzerland , Ireland

Saturday, 14 October 2023

Food Truck - kitchentruck - burger gourmets (location food truck, privatisation food truck

 

C'est une invitation à la découverte de saveurs uniques, à la dégustation de produits d'exception et à l'exploration d'une cuisine créative. Notre passion pour la gastronomie se reflète dans chaque plat que nous préparons, dans chaque ingrédient que nous choisissons et dans chaque sourire que nous voyons sur le visage de nos clients comblés. Rejoignez-nous dans cette aventure culinaire extraordinaire. Chez Kichtentruck, nous ne laissons rien au hasard. Pour accompagner nos burgers gourmets, nous préparons des frites croustillantes faites maison et des salades fraîches, le tout fait maison avec amour. Contactez nous de suite pour une location de food truck une privatisation de food truck, un évènement, un mariage, un anniversaire ou autre. Nous sommes la solution à votre recherche de Food Truck !

Friday, 13 October 2023

Couvreur 95 - Couverture Mayer Charles

 

Votre Couvreur 95 est un artisan couvreur de Père en Fils depuis plusieurs générations, spécialiste de la pose, de la réparation, de l'isolation et de l'entretien des toitures dans le Val d'Oise.

La couverture de toiture est la partie la plus extérieure de la toiture. Réalisée en tuile, ardoise ou zinc, elle doit assurer l'étanchéité du toit et résister aux intempéries (vent, grêle…) ainsi qu'aux diverses agressions (chute de branches, passage d'animaux…).

Thursday, 12 October 2023

Colombo & Silva - Dental Clinic [Almancil]

 

Phone Number:
+351 963 339 346

Business Full Address:
R. Salgueiro Maia 1A, 8135-123 Almancil, Faro, Portugal

Business Email
info@colombosilva.pt

Website Link:
https://colombosilva.pt/

Time
Monday to Friday from 9am to 7pm Saturday from 10am to 2pm

Description:
Clínica dentária especializada em reabilitação com implantes dentários e tratamentos ortodônticos invisíveis Invisalign® Os médicos Glória Silva e Juan Colombo estão a abrir a sua segunda clínica no Algarve com a intenção de oferecer os seus serviços à população do Sotavento Algarvio. Juntamente com a sua equipa de médicos, assistentes e pessoal administrativo, estão empenhados em oferecer tratamentos dentários de qualidade não só à população de Almancil, mas também às cidades vizinhas como Quarteira, Loulé, Faro, Olhão e outras.

Keywords:
invisalign, implantes dentarios, dentista, algarve, almancil, loule, faro, albufeira, quarteira, facetas dentarias, dentist, dental implant, dentist near me

 

Category:
Clínica dentária, Dentista, Clínica de implante dentário, Ortodontista

 

https://www.facebook.com/dentista.lagoa.algarve/

https://twitter.com/DentalHubPT

https://www.instagram.com/clinicadentaria.colomboesilva/

https://maps.app.goo.gl/irpZUoGMfYUucFui7

https://www.linkedin.com/company/colombo-silva-dental-clinic

 

Tuesday, 10 October 2023

Macro Headshots

 

195 US-46 Suite 9
Totowa, NJ 07512, United States

646-244-7282

https://macroheadshots.com

 

Monday 10 am–6 pm

Friday 10 am–6 pm


At Macro Headshots, we use state-of-the-art equipment and techniques to capture stunning and unique headshots that are tailored to your needs. Macro Headshots is run by MacroHype. Our studio is located As a professional headshot studio in Totowa, New Jersey, we offer a variety of packages and styles, including corporate headshots, acting headshots, and more. Our team is dedicated to providing a comfortable and relaxed environment, so you can feel confident and at ease during your headshot session. Whether you’re an aspiring actor, a business professional, or simply looking to update your online presence, we can provide you with high-quality headshots that truly capture your personality and professionalism. Contact us today to schedule your session and experience the difference for yourself. Let us help you take your professional image to the next level!

Headshots
Professional
Photography
Authenticity
MacroHeadshots
PersonalBrand

Couvreur Toulon 83 | Entreprise toiture Toulon | Couvreur Var

https://g.page/r/CQv-EDNS2c0KEBM/review

Couvreur Toulon : Mr Beautour,  Artisan couvreur Zingueur, est recommandée à Toulon et aux alentours depuis plus de 35 ans.

Une passion pour le métier de Couvreur de père en fils et un savoir-faire en rénovation de toiture transmis de génération en génération. Une équipe familiale de passionnés formés au métier de couvreur font le bonheur des clients chaque jour à Toulon (83) et dans un périmètre de 40 kms aux alentours.


Une Entreprise de
Covertures qui donne entière satisfaction à chaque projet qu’il entreprend pour ses clients.

Artisan Couvreur - Spécialiste Toiture - Couverture 31 - Couvreur Toulouse - Couvreur Blagnac - Colomiers et alentours

 


Roofer Marseille 13 , it’s a craftsman for over 30 years with extreme attention and know-how that you only find with an experienced Roofer Zinc Worker like him.

MrBeautour - Marseille roofer has know-how and experience in roofing - roofing in Marseille. Many years of practice in the profession serving its customers. Guaranteed work and quality service with the lowest prices on the market.

Are you looking for a leading roofing company in Marseille? Roofer Marseille .

Monday, 9 October 2023

Couverture AS - Couvreur 95 - Stephane Amette

 Couvreur Pontoise est une entreprise familiale de couvreur, de Père en Fils depuis des années. Un couvreur recommandé à Pontoise 95 car très professionnel, sérieux et efficace dans son travail. Une connaissance dans tous types de toiture et charpente. Un artisan proche de chez vous avec Couvreur Pontoise . Contactez-nous !



Couvreur Pontoise  est expert de votre maison. Isolation, Charpente, Toiture, Gouttières, ravalement de façade, chaque intervention est prise avec les normes de sécurité et dans le respect du travail de qualité d'un Artisan.


Quand on fait appel à Couvreur Pontoise c'est un gage de qualité pour son projet de rénovation, nettoyage, pose ou tout autre en rapport avec votre maison. Couvreur Pontoise  est spécialisé dans le remplacement des tuiles ardoise ou autre, toiture en pente, et quelle que soit la partie de votre maison avec une toiture à remplacer Couvreur Pontoise saura intervenir dans les meilleurs délais.  Contactez nous !



 

Votre Entreprise de Toiture 94 c'est sans aucun doute : Couvreur 94 - MSC TOITURES .
Dans le 94 Val de Marne, si vous avez des projets de Toiture-Couverture-Toit un seul artisan couvreur pourra répondre à vos attentes : Un Couvreur charpentier Zingueur expérimenté et recommandé depuis des années.


Un travail et une passion de Père en fils.


Le métier de Couvreur c'est un métier très complet, cela exige de connaître les règles de sécurité car il travaille en hauteur et bien connaître tous les matériaux et techniques de travail.

 

Tuesday, 3 October 2023

Overcoming ChatGPTs inaccuracies with Pre-Trained AI Prompt Engineering Sequencing Process

 Abstract - In the scientific world, artificial intelligence (AI) has emerged as a paradigm-shifting tool with the promise to speed up and improve human inquiries in ChatGPT. One such AI-based system that is increasingly being discussed and modified to respond to human inquiries is ChatGPT, a well- known language model. OpenAI's ChatGPT, which replicates human interaction by understanding context and producing suitable responses, was trained using enormous volumes of data. It has attracted a lot of interest because of its capacity to efficiently respond to a wide range of human inquiries. Its fluent and thorough responses outperform earlier public chatbots in terms of security and utility. However, there are some issues and restrictions that must be resolved, just like with any technology. This study focuses on the difficulties and restrictions ChatGPT encounters when used with OpenAI. This essay will look at a variety of ChatGPT usage cases. In general, this work seeks to shed light on the difficulties and restrictions of the ChatGPT AI combination. Large language models have been shown useful in a variety of domains. However, a thorough examination of ChatGPT's shortcomings is scarce, thus this study focuses on that issue. The shortcomings of LLMs (Large Language Models), as well as hallucinations, are given and analyzed. These shortcomings include logic, factual errors, math, coding, and bias. Additionally, ChatGPT's drawbacks, restrictions, and social ramifications are discussed. This study aims to help researchers and developers improve chatbots and language models in the future. I'll also look at ChatGPT's restrictions for my research, and I'll break down these difficulties into three groups. With the help of a thorough pre-trained language model, ChatGPT is able to quickly comprehend user inquiries and produce responses that sound natural. ChatGPT can produce new text based on the patterns it has identified from the training data because it has been trained on a sizable corpus of text. Various domains of responses can be It becomes challenging to tell if they were authored by a person or not since they are so convincing. With  little to no direction, it can produce complex essays and poems, workable code, and even web pages and charts based on text descriptions. ChatGPT has established itself as a potential rival to the popular Google search engine thanks to its excellent results.   

Key Words:  artificial intelligence; ChatGPT; Large Language Models, ChatGPT, ChatGPT Failures, Chatbots, Dialogue Systems, Conversational Agents, Question Answering, Natural Language Understanding   

1. ChatGPT Failures  

In this study, we examined ChatGPT's flaws and emphasized its restrictions. Despite its amazing powers in some tasks, it still needs to be improved to thrive in areas like thinking, solving mathematical problems, minimizing bias, etc. Currently, ChatGPT is still prone to these errors. Due to the ambiguous capabilities of the present technology, it is doubtful whether these constraints can be overcome. Future models of ChatGPT and its dependability are also under scrutiny. Although ChatGPT has been evaluated in-depth in this study, there are still certain issues that require improved AI prompts rather than just input prompting. Large language models may accurately describe language from a broader perspective, but it is not clear if they can adequately represent the human mind. I used AI prompting to ask the questions as an example. According to our research, ChatGPT appears to perform very well when it comes to responding to questions involving common sense thinking. To corroborate this observation, additional systematic analysis is needed. • There is no mechanism for ChatGPT to indicate when it is unsure of an answer. Sometimes, it might confidently provide inaccurate answers. Further development is required to enable ChatGPT to convey the degree of trust in its responses. • The responses from ChatGPT are inconsistent and occasionally contradicting. Its responses can differ when the same question is posed. • In this analysis, I looked into ChatGPT's shortcomings from a high level. • Making huge language models open source can help in understanding these models better and addressing their flaws.  

Additionally, because the training set is inaccessible, it is challenging to tell whether ChatGPT has seen a specific query before. Using cases that are exceedingly unlikely to have been seen before by the model is one potential approach for testing ChatGPT.  2. Study on Continuous Learning of AI training model with prompts Sequencing Process   Only the quality of the prompts you provide when utilizing AI tools like ChatGPT determines how well they respond and how easy they are to use. In marketing and sales, there are many Done-for-you (DFY) prompts available. These DFY prompts might not quite match the results you anticipate from a chatbot or your user scenarios. The majority of the time, these questions 

  

© 2023, IJTES       |                                     Volume 03 || Issue 03 || July 2023                                            | Page 17  

are short, general-purpose sentences or phrases. In this study, we'll demonstrate how to use ChatGPT to generate the ideal prompt for any task. You'll discover that a solid prompt could include practice questions.  

What an Inquiry is. The prompt is a text or image input that instructs the AI model what to do and how to respond. For instance, in the case of a language model like GPT3, the prompt may be a brief passage that serves as the basis for the creation of a lengthier passage. The prompt could indicate the subject matter or voice of the information the AI model should produce.  

Instead of requesting ChatGPT to properly compose the email, for instance, we are attempting to write an Outreach email for a social media marketing agency. I'll ask ChatGPT to provide an instruction manual on how to craft the ideal cold outreach email. So, my first prompt is.  2.1. Question: 1st Prompt  

How can I write the perfect cold Outreach email to a potential client selling my social media marketing agency which includes marketing on Facebook, Instagram, Ticktock, Twitter Snapchat? What should I include in the email to better convince the potential client?  

What an Instruction is. The AI model receives instructions from the prompt, which might be a word or image, about what to do and how to respond. A brief passage of text may serve as the prompt in the case of a language model like GPT3 to generate a longer passage of text. The prompt may outline the topic, tone, or style of the final product that the AI model should produce.  

As an illustration, rather than asking ChatGPT to properly compose the email, we are attempting to write an Outreach email for a social media marketing agency. I'll ask ChatGPT to put up a tutorial on how to craft the ideal cold email.  2.2. Question: 2nd Prompt  

Can you write me the exact cold Outreach email I can send to a potential client to hire my social media marketing services highlighting that my agency can help them market on Facebook Instagram Twitter Tiktok and Snapchat using bullet points where appropriate and writing in a simple, but convincing and professional tone?  

Now that the response has improved in quality, personalization, and detail, all we need to do is replace the text's parenthesized words and phrases with our information to utilize the content that has been generated.  2.3. Another example  Imagine that we wish to write about a specific marketing activity, such as sales marketing, on a specific website, such as jvzoo.com. We would use a somewhat different structure for our prompts if we were to prepare the chatGPT AI model before beginning the actual conversation. We are interested in producing a report for a giveaway that explains how new 

affiliates can get started and flourish on the jvzoo.com network. Therefore, we would start by inquiring about chatGPT's familiarity with Jvzoo and affiliate marketing. So, here is how the first prompt would begin.  2.4. Question: 1st prompt   

Do you know what affiliate marketing is?  

then We will ask about the jvzoo platform  2.5. Question: 2nd prompt   

How about the jvzoocom platform? Do you know what it is?  

The third prompt is now available: Please explain how to be a successful new affiliate marketer on the jvzoo.com network.  2.6. Question: 3rd prompt  What steps should a new affiliate marketer who recently signed up on the jvzoo.com platform do to succeed? List all the steps a new affiliate marketer should take on this platform in bullet points, and explain each step, in detail.  2.7. Question 4th Prompt  The next assignment is to design a table of contents for a book that instructs a new affiliate how to begin and succeed on the jvzoo.com platform using the methods you just explained. Please put the title of the book in clear, understandable terms and divide the table of contents into chapters.   2.8. Question 5th Prompt  Therefore, once it has finished creating the report's table of contents, we can simply instruct it to create Chapter 1 and Chapter 2 when it is finished, and so on until it has finished writing all of the book's chapters. At that point, we can copy everything out and format it into a finished book. We have completed the two examples from them. As you can see, the prompts we used are now longer, better, and more specific. In some instances, like in the second example, we had to ask ChatgGPT if it understood our intended topic before instructing it to produce the text. In the second example, we can exclude the first two prompts, which were just intended to prepare the model and get it ready for a higher-quality response, if we are managing our tokens, especially for those on ChatGPT Plus subscriptions. In order to get ChatGPT to produce the greatest possible response for us, we must carefully develop the correct and high-quality prompts for every activity. In our AI- assisted content production efforts, we can now make better prompts.  3. Based on the study and the above examples and proposing the AI Prompt Engineering and Proprietary Continuous Learning AI Training Model  Examples of Continuous Learning Text, graphics, video, and audio are just a few of the outputs that generative AI can 

  

© 2023, IJTES       |                                     Volume 03 || Issue 03 || July 2023                                            | Page 18  

produce. The models are still being developed as ChatGPT continues to learn from user feedback (as shown in the example below). For instance, GPT3.5, the foundation upon which ChatGPT is based, passed the bar in the 10th percentile, whereas GPT4.0, the revised version, now passes in the 90th percentile.  4. Continuous Learning AI Training Model with Prompts Sequencing Process  Step 1: Continuous Training [Fig.1] Aside from the most current data collected after 2022, ChatGPT learns from any information found on the internet, including Wikipedia, online pages, and other sources.  Step 2: User input prompt  Enter what you wish to know or have done for you in the same way as you would in Google Search. How do I cook pancakes, for instance? Write a poem in the style of Woody Allen for Valentine's Day.  Step 3: GPT output GPT will respond to your inquiry or request. For instance, "First you put 100g of flour..." Roses are red, etc.  Step 4: User feedback Give a thumbs up or down to rate the output, or specify or alter the prompt. For instance, "How can I cook pancakes for a mom watching her weight when there are no eggs in the fridge?"  Step 5: GPT updated output Hopefully, GPT will give you a response that is more in line with what you want.  Step 6: User edit/judgment Analyze the content's quality (text, image, etc.) and, if necessary, edit the question once more.  

It is suggested that the ChatGPT AI model be continuously pre- trained using the AI Prompts Sequencing Process in order to reduce failures, errors, and restrictions in ChatGPT's output.   5. Conclusions  To sum up, ChatGPT can help in a wide range of new study areas, and we are just beginning to explore the extent of its potential applications. I have no doubt that artificial intelligence (AI) tools will fundamentally alter every industry, including science. However, difficulties with LLMs and hallucinations present numerous difficulties. ChatGPT has been constrained thus far by computational limitations. All those constraints could result in misunderstandings or incorrect interpretations. Researchers are working hard to overcome these issues and enhance the model's accuracy and dependability. The creation and effectiveness of language models like ChatGPT have been significantly impacted by new technologies and developments in AI.  For instance, modern AI methods like deep learning and neural networks have made it possible to develop more accurate and sophisticated language models that can handle enormous amounts of data and learn from it. Furthermore, the emergence 

of big data and cloud computing has created new opportunities for applications like chatbots, virtual assistants, and language translation by enabling the training and execution of language models at scale. Additionally, pre-trained language models like GPT-3 have lowered the amount of data and computing power needed to train new models, making it simpler for academics and developers to design their own language models. For instance, working with linguists can help to improve language models by incorporating a deeper comprehension of the subtleties of human communication and language. Working with computer scientists can result in the creation of more effective and efficient training and running algorithms for language models. The two instances below exemplify what we refer to as the "Prompts Sequencing Process," which is a revolutionary and proprietary continuous training AI model that is proposed. a series of prompts designed to produce the best outcomes currently possible from AI, starting with an initial prompt and progressing logically through a set of following prompts. So thorough prompt engineering is required to get an ideal result. Users will be happier with their interactions with AI models if the prompts are more pertinent and meaningful. For individuals who use AI models, this will result in a more gratifying experience.   

REFERENCES  

Journal Papers  1. ChatGPT Sprints to One Million Users. Available online: https://www.statista.com/chart/29174/time-to-one-million-users/ (accessed on 10 March 2023). 2. ChatGPT Reaches 100 Million Users Two Months after Launch. Available online: https://www.theguardian.com/technology/20 23/feb/02/chatgpt- 100-million-users-open-ai-fastest-growing-app (accessed on 10 March 2023). 3. Turing, A.M. Computing Machinery and Intelligence. Mind 1950, 236, 433–460. https://doi.org/10.1093/mind/LIX.236.433 4. Thorp, H.H. ChatGPT Is Fun, but Not an Author. Science 2023, 379, 313. https://doi.org/10.1126/science.adg7879 5. Kirmani, A.R. Artificial Intelligence-Enabled Science Poetry. ACS Energy Lett. 2022, 8, 574–576. https://doi.org/10.1021/acsenergylett.2c02758 6. Grimaldi, G.; Ehrler, B. AI et al.: Machines Are About to Change Scientific Publishing Forever. ACS Energy Lett. 2023, 8, 878–880. 7. Buriak, J.M.; Akinwande, D.; Artzi, N.; Jeffrey Brinker, C.; Burrows, C.; Chan, W.C.W.; Chen, C.; Chen, X.; Chhowalla, M.; Chi, L.; et al. Best Practices for Using AI When Writing Scientific Manuscripts. ACS Nano 2023, 17, 4091–4093. 8. Frieder, S.; Pinchetti, L.; Griffiths, R.; Salvatori, T.; Lukasiewicz, T.; Petersen, P.C.; Chevalier, A.; Berner, J. Mathematical Capabilities of ChatGPT. arXiv 2023, arXiv:2301.13867.  

  

© 2023, IJTES       |                                     Volume 03 || Issue 03 || July 2023                                            | Page 19 

Guiding AI with human intuition for solving mathematical problems in Chat GPT

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/373447147

 1.      Abstract

Finding patterns and using them to create and support conjectures, or theorems, is a key component of mathematics practice. Computers have been used by mathematicians to help with pattern recognition and conjecture generation. Here, we show how machine learning can help mathematicians come up with new conjectures and theorems by giving cases of new basic findings in pure mathematics found with its assistance. We recommend using attribution approaches to recognize probable patterns and connections among mathematical objects, after which you may use these discoveries to guide your intuition and offer presumptions in ChatGPT. We initiate this machine-learning- guided structure and demonstrate how it can be successfully applied to recent research questions in several regions of pure mathematics errors and hallucinations in ChatGPT, in each case illustrating how it led to important mathematical advances on crucial key challenges: a new link between the algebraic and feature extraction techniques of knots, and a candidate algorithm anticipated by the perfect blend in-variance conjecture for symmetries. Our study might be used as an illustration of how mathematics, artificial intelligence (AI), and ChatGPT can cooperate to generate unexpected outcomes by exploiting each other's unique strengths.

Pattern recognition and the formation of relevant hypotheses—statements that are presumed to be true but have not yet been


shown to hold in every situation—are two of the main forces behind mathematical advancement. Two of the most important drivers of mathematical progress are the discovery of structures and the formulation of useful conjectures, which are hypotheses that are assumed to be true but have still not been demonstrated to apply in all circumstances. Mathematicians have always utilized data to aid in this procedure, whether it is the early hand- calculated prime tables employed by Gauss and others that resulted in the ―prime number theorem‖ or more current computer-generated data in situations like Birch and Swinnerton- Dyer conjecture. Thanks to the invention of computers to create data and test ideas, mathematicians today have a fresh understanding of earlier insoluble issues. Even while computational approaches have continually been effective in other elements of mathematical course, artificial intelligence (AI) systems have still not established a similar position. A variety of techniques for reliably finding patterns in data are provided by AI, particularly  the  study  of  machine  learning, and its applicability in several scientific fields is expanding. AI has shown that it can be an effective instrument in mathematics by producing symbolic answers, speeding up computations, and spotting the existence of structure in mathematical objects. Here, we demonstrate how the AI model of ChatGPT may also be utilized to uncover cutting-edge theorems and hypotheses in mathematical research. This extends work utilizing

supervised learning to detect patterns by emphasizing making it feasible for mathematicians to interpret the learned functions and draw efficient mathematical ideas in ChatGPT. We introduce a methodology for extending the typical mathematician's toolset, which includes sophisticated pattern categorization and interpreting algorithms derived from "machine learning", and we show its value and generalization by showing how it assisted us in making two advancements, one in topology and another in representation theory. To create innovative findings in ChatGPT, our work exhibits the flexibility and fusion of well- known mathematical operations with existing machine-learning approaches.


1.      Guiding mathematical intuition with AI

 

A mathematician's intuition is vital to mathematical discovery because "complex mathematical problems can only be approached with a combination of both rigorous formalism and good intuition." The guideline that follows, illustrated in Fig. 1, provides an overview of a general strategy that mathematicians can practice    machine    learning‖    techniques   to instruct their gut feelings regarding complicated mathematical artifacts, authenticating their hypotheses about the presence of relationships and assisting them in acknowledging those connections.


 

 

 

Flowchart  of  the  framework,  Fig.  1.  By  teaching  a  machine  learning  model  to  estimate  a  hypothetical  f(x  over  a  certain  data distribution PZ, the approach aids a mathematician's understanding. The comprehension of the issue and creation of a closed-form f′ can benefit from the revelations from the correctness of the learned function f and the attribution techniques used to it. Instead of being a linear process, iteration and interaction characterize the procedure.‖

 

 


We argue that this is a logical and experimentally successful approach for mathematicians to apply these well-known statistics and machine learning‖ techniques in their study. Mathematicians can strengthen their understanding regarding the connection between two mathematical objects, X(z) and


Y(z) associated with z, by locating a function f such that f (X(z)) Y(z) and examining it. We contend that using these well-known statistics and ―machine learning‖ approaches in mathematical research is a logical and experimentally winning approach. By discovering and analyzing a function f such that


 

 


f (X(z)) Y(z), mathematicians can better comprehend the affiliation between two mathematical objects X(z) and Y(z) related to z. The properties of the connection can then be understood by the mathematician. Assume that z is a convex polyhedron, with X(z) Z R 2 2 representing its vertex, edge, volume, and surface, and Y(z) Z representing its face count. This offers an illustration. The connection between X(z) and Y(z) in this case is accurate according to Euler's formula: X(z) (1, 1, 0, 0) + 2 = Y (z). Among several additional examples, the link might be recovered by employing the standard methods of data-driven speculation generation1. For X(z) and Y(z) in higher- dimensional spaces, or of more complicated forms, such as graphs, and for more complex, nonlinear f, this strategy is either less successful or altogether unworkable. This process helped mathematicians identify patterns in mathematical objects by utilizing attribution methods and supervised machine learning‖ to corroborate the similarities that have been theorized to occur in mathematical objects. During the guided learning phase, the mathematician claims that X(z) and Y have a connection (z). By building a dataset containing X(z) and Y(z) pairings, We can deploy supervised learning. to develop a function f that predicts Y(z) using only X(z) as an output. The primary advantages of ―machine learning‖ in this cointegration procedure are numerous nonlinear functions that may be identified with sufficient data. If f is more precise than would be expected by chance, this raises the possibility of such a link and should be looked into. In this situation, attribution strategies can help the mathematician understand the learned function f so they can suggest a contender, f′. Employing attribution approaches, one may


identify the features of f that are crucial for Y prediction (z). Many attribution strategies, for example, goal to compute the portion of X(z) that the function f is responsive to. Attribution technique we use in our work, gradient saliency, does this by calculating the derivative of the outcomes of f concerning the intakes. As a result, it is feasible for a mathematician to identify and tier the characteristics of the phenomenon that would be most significant to the connection. This iterative approach might have to be conducted numerous times before a viable hypothesis is selected. This procedure can be guided by the mathematician by choosing hypotheses that, despite fitting the facts, also strike them as fascinating, tenable, and, ideally, indicative of a proof method. From a conceptual perspective, this framework provides a "test bed for intuition" by immediately identifying if an intuition about the connection between two variables may be interesting to explore and, if so, providing direction on how they may be connected. It is possible that this iterative approach needs to be done numerous times before a viable hypothesis is selected. This procedure can be guided by the mathematician by choosing hypotheses that, in addition to fitting the facts, also strike them as fascinating, tenable, and, ideally, indicative of a proof method. From a conceptual perspective, this framework provides a "test bed for intuition" by immediately identifying if an intuition about the connection between two quantities may be interesting to explore and, if so, providing direction on how they may be connected. Using the abovementioned approach, we have developed one of the earliest linkages between algebraic and geometric invariants in knot theory and postulated solutions to the well-known combinatorial invariance


 

 


conjecture for symmetrical groups in representation theory. We demonstrate each instance when the paradigm effectively assisted the mathematician in arriving at the correct conclusion. The required models for each of these cases may be trained in a couple of hours on a computer with a single graphics processing unit.

 

2.      Topology using one graphics processing unit.

 

Low-dimensional topology is a significant branch of mathematics. The knot, a straightforward closed loop in the third dimension, is one of the principal subjects investigated. One of the primary study objectives is to classify knots, learn about their features, and relate them to other subjects. One of the primary techniques for doing this is the use of invariants, which are algebraic, geometrical, or numerical properties that are same for any two equal knots. These invariants can be consequential in a variety of methods, but we focus on two of the most common: algebraic and hyperbolic invariants. Because these two categories of invariants originate from quite dissimilar areas of mathematics, it is important to build connections between them. A few examples of these invariants for tiny knots are shown in Figure 2.


A famous case of a conjectured link is the volume conjecture, which states that hyperbolic volume of a knot (a geometric invariant) should be stored inside asymptotic behavior of its colored Jones polynomials (which are algebraic invariants). We assumed that there is an unrecognized link between a knot's algebraic and hyperbolic invariants. By using supervised learning, it was discovered that a huge number of geometric invariants and the signature (K), which is known to store crucial information about a knot K but had hitherto been unrelated to hyperbolic geometry reflect a trend.

Three cusp geometry invariants were the most notable traits identified by the attribution approach; Fig. 3b partially shows their relation. Figure 3a depicts these characteristics. Research demonstrates that constructing a second model using X(z) including simply of these measurements leads to very comparable accuracy, indicating that these data are a sufficient set of characteristics to capture virtually all of the influence of geometry on the signature. The longitudinal translation and the real and fictitious parts of meridian translation consisted of these three invariants. The relationship between these factors and the signature is nonlinear and multivariate. After being asked to focus on these invariants, we found that the easiest way to understand this connection is to use a new number that is linearly connected to the signature.


 

Fig.  2  |  Examples  of  invariants  for  three  hyperbolic  knots.  We  hypothesized  that  there  was  a  previously  undiscovered  relationship between the geometric and algebraic invariants We introduce the concept of natural slope‖, which is defined as slope(K) = Re(/), where Re stands for the real part. It can be interpreted geometrically as follows. The meridian curve can be visualized as a geodesic on the Euclidean torus. From this orthogonally, if one fires a geodesic, it will eventually return and hit at some point. It will have done so by traveling along a longitude that is less than a certain multiple of the meridian.‖

 


We introduce the idea of "natural slope," which is described as slope(K) = Re(/), where Re stands for real component. It may be interpreted geometrically as follows. The meridian curve can be shown as a geodesic on Euclidean torus. From here orthogonally, if one launches a geodesic, it will ultimately return and hit at some location. It will have done so along a longitude that is less than a certain multiple of meridian. This number represents the natural slope. It may not have been an integer because the terminus and beginning point could not be the same. Our first theory on the natural slope and signature were as follows.

Theorem: For each hyperbolic knot K, |2 K() slope() K c | vol(K c) + (1) 1 2 is a feasible value of the constants c1 and c2.

Although this hypothesis was validated by an examination of multiple substantial datasets selected from different distributions, we were able to produce counterexamples by employing braids of a certain kind. This figure naturally represents the slope. It need not be an integer because the terminus could not be the same as the beginning point. The following were our


first presumptions on the natural slope and signature.

It is believed that constants c1 and c2 occur such that for any hyperbolic knot K, |2 K() slope() K c | vol(K c) + (1)

Although this hypothesis was validated by an examination of numerous big datasets taken from diverse distributions, we were nevertheless able to produce counterarguments utilizing braids of a certain sort. Reference 27 offers further details and a comprehensive demonstration of the abovementioned theorem. For the datasets we produced, we may establish a lower bound of c 0.23392, and it is reasonable to believe that c is at most 0.3, which leads to a close association in the locations where we have computed.

 

Reference 27 provides further details and a thorough demonstration of the aforementioned theorem. For datasets we produced, we may establish a lower bound of c 0.23392, and it makes sense to suppose that c is at most 0.3, resulting in a close association in the areas where our computations have been performed.


3.      Representation theory

 

Representation theory is the name given to the theory of linear symmetry. Understanding the fundamental components, which form the basis of all representations, is one of the fundamental objectives of representation theory. By redundant representations28, basic frequencies of Fourier analysis are generalized. In numerous important circumstances, form of irreducible representations is governed by Kazhdan-Lusztig (KL) polynomials, which are strongly connected to combinatorics, algebraic geometry, and singularity theory. KL polynomials are connected to pairs of elements and are symmetric group polynomials (or more generally, pairs of elements in Coxeter groups).

 

 

 

 

 

 

 

 

 

 

 

 

 


Figure  4  shows  two  sample  dataset  elements  from  S5  and  S6,  respectively.  The  KL polynomial  of  a  pair  of  permutations  should  be computed from their unlabeled Bruhat interval, according to the combinatorial invariance conjecture, but no such function was previously known.‖


The combinatorial invariance conjecture regarding KL polynomials is a fascinating open conjecture that has only made some progress over the past 40 years. It asserts that KL polynomials of two components in a symmetric group SN may be determined using the unlabeled Bruhat interval30, a directed graph. One barricade to comprehending the link between these items is the size of the Bruhat intervals for non-trivial KL polynomials (those that are not equal to 1), which makes it difficult to acquire an understanding of them. The combinatorial invariance hypothesis, an intriguing unsolved conjecture involving KL polynomials, has been around for 40 years with only incomplete results29. It asserts that the KL polynomial of two elements in a symmetric group SN may be calculated from the directed graph of the unlabeled Bruhat interval30 of those two components. One of the obstacles to advancement in examining the relation between these items is the very large graphs of the Bruhat intervals for non-trivial KL polynomials (those that are not equal to 1Additional structural evidence has emerged by constructing salient subset that attribution


techniques decided were most relevant and comparing The edge distribution within those graphs is identical to the earlier graphs. As per the reflection that each of those edges in Fig. 5a represents, we combine the relative frequency of the edges in salient subgraphs. Opposite to predictions, it indicates that extremal reflections—those for SN of the type (0, I, or I N 1)—appear more commonly in salient subgraphs than simple reflections—those for SN of the form I I + 1. This conclusion is confirmed by multiple model retraining in Fig. 5b. This is important since it prevents recovery of the edge labels or the unlabeled Bruhat interval. Although it was first not evident why extremal reflections would be more common in salient subgraphs, the gap between simple and non-simple reflections is crucial for computing KL polynomials. We discovered that an interval can automatically split into two pieces by taking into consideration this observation: a hypercube formed by one group of extremal edges and a graph that is isomorphic to an interval in SN1.


 


Fig. 5 | Attribution in the representation theory. An illustration of a heatmap showing how much more reflections is present in the salient subgraphs when compared to the dataset's average across intervals when predicting the fourth quarter. b, the proportion of edges of each type that were observed in the salient subgraph across 10 model retraining as compared to 10 bootstrapped samples of the same size from the dataset. A two-sided, two-sample t-test was used to calculate the significance level, and the error bars represent 95 percent confidence intervals. *p 0.05; ****p 0.0001. c, Illustration of the interesting substructures found through the iterative process of hypothesis, supervised learning, and attribution for the interval 021435-240513 S6. The hypercube is highlighted in green; the decomposition component is highlighted in red and the paragraph's inspiration from earlier work31‖

 

 


using representation theory to distribute. An example of a heatmap demonstrating the difference between average across intervals of dataset and the salient subgraphs when predicting q4. b, The measured edge % for each edge type in the salient subgraph for 10 models retraining are shown in contrast to 10 bootstrapped samples of the same size from the dataset. A two-sided, two-sample t-test was used to determine the level of significance, and the error margins show 95 % confidence intervals. Demonstration for the fascinating substructures revealed through the iteratively of hypothesis, supervised learning, and attribution in range 021435-240513 S6. *p 0.05; ****p 0.0001. The subgraph was influenced by prior work31, and the hypercube is indicated in green while the decomposition element is shown in red. This has been computationally proven for more than 1.3 105 non-isomorphic intervals taken from the symmetric groups S8 and S9 and for all 3 106 intervals in the symmetric groups up to S7.I assert that it is possible to determine KL polynomial of an unlabeled Bruhat interval using any hypercube decomposition. This suggested solution would refute the combinatorial invariance conjecture for symmetric groups if it were proven to be correct. This is an intriguing direction since the hypothesis has been experimentally proved up to pretty big cases, and it also has a particularly appealing shape that offers various ways of tackling the problem. This illustration


demonstrates how trained models may provide non-trivial insights into the behavior of significant mathematical objects, resulting in the identification of novel structures.

 

4.      Conclusion

 

These are some of the earliest linkages among knot algebraic and geometric structure and a suggested solution to a long-standing open problem in representation theory. are two examples of how this work illustrates a framework   for   mathematicians   to   practice

machine learning‖. Instead of using machine learning‖ to create conjectures directly, we concentrate on assisting the highly developed intuition of skilled mathematicians, producing both interesting and profound results. Using human intuition to guide AI in ChatGPT to solve mathematical issues, errors, and hallucinations. It is evident that elite performance in many areas of human endeavor greatly benefits from intuition. Similar to how it is regarded as essential for top mathematicians, Ramanujan—known as the Prince of Intuition—has                           prompted        famous mathematicians to consider its role in their discipline. Since mathematics is a very different and more collaborative endeavor than Go, ChatGPT's use of AI to support intuition is much more logical. Here, we demonstrate that there is space that can help mathematicians in this area of their work. Our case studies show


 

 


how framework aids mathematicians in better understanding the behavior of objects too vast for them to perceive patterns in mathematical problems to solve. They also show how a foundational connection in a well-studied and mathematically interesting area can go unnoticed. The applicability of this framework is constrained because it necessitates the production of sizable datasets of object representations and the detection of patterns in calculable examples. Additionally, the functions of interest in some domains might be

 

5.      References

 

1.    Borwein, J. & Bailey, D. Mathematics by Experiment (CRC, 2008).

2.     Birch, B. J. & Swinnerton-Dyer, H. P. F. Notes on elliptic curves. II. J. Reine Angew. Math. 1965, 79–108 (1965).

3.      Carlson, J. et al. The Millennium Prize Problems (American Mathematical Soc., 2006).

4.      Brenti, F. Kazhdan-Lusztig polynomials: history, problems, and combinatorial invariance. Sémin. Lothar. Combin. 49, B49b (2002).

5.    Hoche, R. Nicomachi Geraseni Pythagorei Introductions Arithmeticae Libri 2 (In aedibus BG Teubneri, 1866).

6.   Khovanov, M. Patterns in knot cohomology, I. Exp. Math. 12, 365–374 (2003).

7.   Appel, K. I. & Haken, W. Every Planar Map Is Four Colorable Vol. 98 (American Mathematical Soc., 1989).

8.   Scholze, P. Half a year of the Liquid Tensor Experiment:    amazing           developments  Xena https://xenaproject.wordpress.com/2021/06/05/ half-a-year-of-the-liquid-tensorexperiment- amazing-developments/ (2021).

9.        Fajtlowicz,    S.    in    Annals    of    Discrete Mathematics Vol. 38 113–118 (Elsevier, 1988).


challenging to learn using this paradigm. However, we think our approach has applications in numerous fields. More generally, we hope that this framework will serve as a useful tool for introducing ―machine learning‖ into mathematicians' work by training AI to solve mathematical problems using human intuition, reducing errors and hallucinations in ChatGPT, and fostering future collaboration between the two disciplines.

K.Capital Realty - Phuket Property Agency

  Address 129 Nanai Road, Patong, Kathu, 83150 Phuket, Thailand Phone +66635834250 Website URL https://kcaprealty.com Business de...