Has the Pandemic Accelerated AI in Healthcare?

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Introduction 

While the pandemic has spurred digital transformation, even a corporate metaverse debate about the future of remote work, AI was not invaluable during the pandemic in fighting against Covid-19 directly. AI should have been able to warn us that a pandemic was coming, but it didn’t. Those few weeks of uncertainty were very costly in how countries prepared for what was to come.

Still AI in healthcare has made many little gains during the last two years, many of which have not been well publicized. As for a warning system of AI for the next pandemic, a recently announced early warning system designed by MedShr Insights may have the capability to predict pandemics. The capability fetched the technology third place honor in the Trinity Challenge and a prize of $660,000.

AI Shows Promise in Early Diagnosis and Detection 

AI has improved in reading various medical scans and tests, to catch what humans miss. Early detection of diseases, dementia and many other conditions and hyper-personalizing the patient experience are certainly the abode of artificial intelligence’s impact on the future of healthcare. AI in pharma and drug discovery also has grown in leaps and bounds.

AI in healthcare is also somewhat controversial. Back in 2019, a group of healthcare specialists created an AI-based system that can predict the risk of premature death caused by chronic disease. For urgent situations where ICUs are full and doctors need to decide which Covid-19 patients to treat first or give priority to, AI should be making the call, as it’s very stressful for people to make those kinds of choices.

Future of AI in Healthcare and Need for Better AI Ethics Highlighted 

AI will certainly be implicated in triage efficiency too, as well as preventative healthcare. Conditions like Long-covid (Long Haulers) will likely enable AI to learn which symptoms are most likely to lead to temporary disability. AI will also be used in the advent of biotechnology, human augmentation and medical ethics and the WHO created important guidelines around the use of AI in Healthcare. I find this fascinating as I think a lot about AI ethics.

What I especially like about the WHO guidelines and report about AI’s impact on healthcare is moderation vs. the hype. Their new ethics guidance cautions against overestimating the benefits of technology. This is important to realize as an abundance of headlines and research doesn’t mean AI is impacting the current reality of healthcare all that much.

The new guidance, Ethics & Governance of Artificial Intelligence for Health, is the result of two years of consultations held by a panel of international experts appointed by the WHO. While the WHO was possibly partly incompetent in certain aspects of the early stage pandemic, their awareness and attempt to make rules around AI’s use for a humanitarian sense is really one of the better models we have.

The World Health Organizations Principles Around AI

What follows is their quote directly from here.

Ultimately, guided by existing laws and human rights obligations, and new laws and policies that enshrine ethical principles, governments, providers, and designers must work together to address ethics and human rights concerns at every stage of an AI technology’s design, development, and deployment. 

Six principles to ensure AI works for the public interest in all countries

To limit the risks and maximize the opportunities intrinsic in the use of AI for health, the WHO provides the following principles as the basis for AI regulation and governance:

1. Protecting human autonomy: In the context of health care, this means that humans should remain in control of health-care systems and medical decisions; privacy and confidentiality should be protected, and patients must give valid informed consent through appropriate legal frameworks for data protection.

2. Promoting human well-being and safety and the public interest. The designers of AI technologies should satisfy regulatory requirements for safety, accuracy and efficacy for well-defined use cases or indications. Measures of quality control in practice and quality improvement in the use of AI must be available.

3. Ensuring transparency, explainability and intelligibility. Transparency requires that sufficient information be published or documented before the design or deployment of an AI technology. Such information must be easily accessible and facilitate meaningful public consultation and debate on how the technology is designed and how it should or should not be used.

4. Fostering responsibility and accountability. Although AI technologies perform specific tasks, it is the responsibility of stakeholders to ensure that they are used under appropriate conditions and by appropriately trained people. Effective mechanisms should be available for questioning and for redress for individuals and groups that are adversely affected by decisions based on algorithms.

5. Ensuring inclusiveness and equity. Inclusiveness requires that AI for health be designed to encourage the widest possible equitable use and access, irrespective of age, sex, gender, income, race, ethnicity, sexual orientation, ability or other characteristics protected under human rights codes.

6. Promoting AI that is responsive and sustainable. Designers, developers and users should continuously and transparently assess AI applications during actual use to determine whether AI responds adequately and appropriately to expectations and requirements. AI systems should also be designed to minimize their environmental consequences and increase energy efficiency. Governments and companies should address anticipated disruptions in the workplace, including training for health-care workers to adapt to the use of AI systems, and potential job losses due to use of automated systems.         

Human Rights in the Metaverse AI-of-Everything World?

In the spirit of digital transformation a lot of progress is actually by-passing certain aspects of our human rights where legal regulation isn’t taking place. It would be a pity if AI’s impact on healthcare were one of these areas where data protection, privacy and the right to personal choice was not implemented in an orderly fashion. Since we know that companies such as Google, Amazon, Apple and others are getting aggressively into healthcare we must be vigilant to maintain a high ethical code of conduct around the impact of AI in healthcare.

While digital transformation has flourished during the pandemic, I don’t think we’ve seen a corresponding explosion of AI in healthcare breakthroughs as we have in other fields such as FinTech, the corporate metaverse (e.g. Microsoft Teams), home fitness or even telemedicine itself as a rapidly maturing industry. AI in healthcare is more ubiquitous but slow moving and becoming more active in academic research and medical R&D such as drug discovery in particular.

Benefits outweigh the Risks for AI in Healthcare

Europe appears to be thinking the most of how AI will impact healthcare among global bodies. Earlier this year, European health innovation network, EIT Health launched an AI report from its Think Tank, urging healthcare providers to invest more in AI and tech post-pandemic. Dozens of health tech startups are also utilizing AI in healthcare solutions and they will mature in the 2020s as will biotechnology companies that scale to the mainstream.

Dr Tedros Adhanom Ghebreyesus, WHO Director General, said: “Like all new technology, AI holds enormous potential for improving the health of millions of people around the world, but like all technology it can also be misused and cause harm. Indeed the abuse of medical data and privacy abuses of technology coming closer to the home (as with remote work) brings up many questions as to AI’s impact on the data harvesting of people with special conditions. If the smart home is to become medically proficient with AI, how do the patients know where their data is going? If an E-commerce retailer knows which meds I get delivered or Apple builds an integrated EMR system, that’s a lot of our sensitive data potentially exposed to third parties.

AI will Soon Personalized Healthcare and Get More Personal as Our Intermediary with the World 

Even more likely than us living in a metaverse is AI being embedded in our world, and dealing with our most intimate mental health, social, cognitive, and health related data. What are our human rights in such a world of AI permeating our health related environments? If my FitBit knows about my sleep patterns, will Google use that information to tailor Ads to me with predictive analytics? The reality of an AIoT world are both amazing and a little frightening. The impact of AI on our mental health life is particularly worrisome.

While technology leads to more loneliness in society as mobile time and streaming time cut into human time, will AI help us one day with a fake solution to our technological loneliness? These are some of the very real human questions around the use of AI in healthcare (much of it in the home) in the future. AI in healthcare has huge implications on major developments such as:

• Adventure of the brain-computer interface (BCI)
• AI’s impact on radiology, early detection scans and Big Data to personalize care
• Improving healthcare accessibility and inclusion to underserved populations and the most vulnerable
• Using predictive analytics on medical history related to family history for significant reduction in early detection of ailments
• Bringing Electronic Medical Records (EMR) into the cloud and tracking much more than typical EMR systems do, with more efficiency and embodied artificial intelligence.
• Dealing with large systemic issues like the rising cost of healthcare, the burden of antibiotic resistance, the problems associated with reduced global fertility rates, the rising percentage of the elderly (not to mention the next pandemic).

Conclusion: AI in Healthcare is Just Beginning 

The pandemic has not been aided by AI by and large, but we have a better frame of reference for what the AI of healthcare will entail in the 2020s and 2030s with many new developments related to healthcare.

The AI of Healthcare will have distinct costs and benefits, and medical professionals will increasingly work in an AI-human hybrid system. Medical devices, machines and robotics (including robotic surgery) will take decades to improve and be refined.

Globally in the 2020s, AI in healthcare is just in its infancy. For data scientists and knowledge workers it’s clear machine learning will become more implicated in the years ahead in making clinical decisions with better data. Medical transcriptions and software that helps doctors reduce their task load is already accelerating at a rapid pace.

Several types of AI are already being employed by payers and providers of care, and life sciences companies. AI is just exploring what’s possible to improve and revolutionize healthcare, improve longevity and make healthcare more affordable and accessible to all. While AI contributes to aspects of dystopia in some ways, AI in Healthcare is one of the key ways that AI can help us move to a world that more resembles a utopia. AI’s impact in healthcare is so radically good the entire narrative of ‘AI for Good’ may hinge upon it.

As for knowledge workers in the datascience and machine learning realm, we will need talent to make AI in Healthcare a reality. The quality of life for millions of people may depend upon it. 

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Top 4 Artificial Intelligence Engineer certifications in 2021

With the high rise in demand for talent in the field of Artificial Intelligence (AI), the need for professionals who have expertise in this field has also increased immensely. Worldwide, many organizations are on the lookout for individuals who possess a great skillsets in the field of AI.

This demand gave rise to the artificial intelligence engineer certification program, which is offered by several online learning institutes. If a person wants to enhance their skill set and also stay ahead in the growing populations then doing a certification program in the field of AI is the best choice.

In this article, let’s understand the most affordable and industry-recognized top AI certifications that one can do to jump the career ladder.

Coursera is a world-class learning platform that offers numerous certification programs in various fields. It has partnered with more than 200 leading universities and many firms to give the most affordable, flexible, job-relevant online learning to the people who want to step up in their careers. Among those, there is a certification program called “AI For Everyone.” This certification program offers in-depth knowledge of AI terminologies like neural networks, Machine Learning (ML), deep learning, and data science. This program provides a better understanding of many AI strategies that are helpful for developing ML and data science projects.

Artificial Intelligence Board of America (ARTiBA) provides Artificial Intelligence Engineer(AIE™) certification. The main objective of this certification program is to empower every professional to enrich their career in the field of AI. The AIE™ certification based on the internationally recognized AMDEX™ framework offers an individual to attain knowledge as Subject Matter Experts (SME) as well as rigorous AI learning and industry-relevant exposure.   

In this AI certification program, one can learn the several concepts of ML, supervised and unsupervised learning, Natural Language Processing (NLP), cognitive computing, reinforced learning, and deep learning. This program is self-paced and is ideal for those who are looking to gain better knowledge. One can appear for an exam after 45 days of registration. This is high-level certification best fits those individuals who want to gain an edge in the field of AI engineering.

This artificial intelligence engineer certification program also provides thorough learning and preparing experience by offering a free learning deck that comprises special resources curated by top-level industry experts. It is specially designed to help applicants to develop necessary skills and acquire job-ready capabilities so that they can step up in their career ladder and grab leadership positions.

• Eligibility

Registrants are needed to fulfill specific prerequisites that are based on education as well as professional experience to be eligible for AIE™ certification. Overall, the registrants can be categorized under the following 3 tracks:

Microsoft offers Professional Program Certification in Artificial Intelligence that provides a comprehensive program of study in the field of AI. A person can explore many areas that include the basics of ML, Language, and Communication, Computer Vision, also learn key programming language-Python. The individuals will also have the freedom to opt between the areas related to Computer Vision and Image Analysis or Speech Recognition Systems or Natural Language Processing (NLP) where they can start leveraging data to develop intelligent solutions.

Simplilearn provides an Artificial Intelligence Engineer certification program in collaboration with IBM. This certification program will enhance the skill set of a person and makes them to gain more expertise in the field of Artificial Intelligence. Each individual can master the concepts of data science with python, ML, deep learning, & NLP with the best features from IBM like hackathons, master classes, live sessions, practical labs, ask me for anything sessions & projects. Registrants will also get access to the IBM Cloud Lite account and Simplilearn AI Master’s Certificate that is industry-recognized globally.

If a person is looking for affordable and industry-recognized certification programs in the field of AI. Then the aforementioned certification programs are the best choice for them. They not only enhance your career but also help to grab a growth-driven job with an attractive salary in a well-established company.

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Machine Learning Meets Deep Learning in Autonomous Vehicles

Transcending human perception, today autonomous vehicles or AVs have become a reality. Auto giants such as Tesla, BMW, Google, Volkswagen and Volvo have been the front runners in introducing autonomous transportation to ease the pressure off. Meanwhile, the market growth for AV or autonomous vehicles is estimated to touch 40% of CAGR, annually in the next six years.

Before going further, it would be worth knowing how vehicles can function autonomously. An AV or autonomous vehicle is equipped with a vision system, LIDAR or radar based sensing and multiple neural networks trained with data and machine learning algorithms. The multi-layer neural network enables the autonomous cars to identify objects and recognize them. This processed data through machine learning algorithms learns about the objects and enables the vehicle to figure out the next move based on the environment. It may sound simple, however, from object detection and recognition to processing of next move, AVs rely on the neural network data, 360 degree view of the environment using 3D point cloud segmentation and object detection using computer vision.

AV levels and ADAS or Advanced Driver Assist System

In some countries like the US, self driving vehicles are regulated as per the technical specification they are equipped with. ADAS or Advanced Driver Assist System, is a driving assistant support mechanism and is the key indicator of level of autonomy an AV is equipped with. There are following autonomy levels delineated under the ADAS:

• Level 1 (DA or driver assistance) includes adaptive cruise control, emergency brake assist, automatic emergency brake assist, lane-keeping, and lane centering.
• Level 2 (POA or partial operation automation) includes highway assist, autonomous obstacle avoidance, and autonomous parking.
• Level 3 (CA or conditional automation) to include highway driving, driver initiated lane change, automated valet parking.
• Level 4 (AOA or advanced operation automation) sustainable and operational design; limited implementation of DDT or dynamic driving task.
• Level 5 is when the vehicle is fully autonomous; no human intervention.

Deep learning: Algorithms, neural network mesh with ADAS inclusion

Object detection, recognition, image localization and prediction of the next movement form the core when it comes to autonomous vehicles. The localization remains a challenging task in autonomous vehicles which enables them to understand its own positioning on the ground. This challenge is dealt with satellite based navigation systems and inertial navigation systems. The ADAS works for long range detection while CNNs play a critical role in lane detection, pedestrian detection and redundant object detection as well.

The CNNs or convolutional neural network are powered by machine learning algorithms that work and process the sensor data in real-time to produce actionable steps of the vehicle. This is an extremely crucial and data-intense operation, and requires fast execution. Therefore, most autonomous vehicles are built with specific hardware requirements based on the multi-format data interaction and simultaneous processing. The hardware requirements include GPU, TPU, FPGA for training and deployment to make the vehicle functional

                                                                       Image credit: researchgate

Autonomous vehicles employ deep learning and there is a concrete reason for this. AVs function on end-to-end learning and everything takes place in real-time, hence the data processing must be at lightning fast speed. The method of processing images for example, applied in the vehicles, wherein, the camera images are directly processed into CNN which reproduces steering angle as output. The deep learning (mesh) is performed by the massive technology structure that enables the vehicle to perceive, plan, coordinate and control. The overall movement of the vehicle encompasses these:

• For perception: Localization or environmental perception
• For plan: Mission, behavior and motion planning
• For control: Path or trajectory tracking       

Combined with machine learning algorithms, the data utilized for processing via deep learning pass through algorithms like pattern recognition methods – SVM or support vector machine with histogram of oriented gradients and PCA or Principle Component Analysis. The clustering algorithm is also utilized to find out the most relevant and appropriate imagery to understand the environment. While, the decision matrix algorithm – Adaboost is used for making overall prediction and decision of car’s movement.

End note

The autonomous vehicles are under trial for a few years. An increased focus on making the movement of the vehicle safe and efficient around the cities across the world can be seen. Pertinently, localization has been the most crucial challenge to work on and the recent development and advancement in the concept of SLAM (Simultaneous localization and mapping) has significantly addressed some of the localization challenges. The perception of the environment of an autonomous vehicle has undergone many changes in the past couple of years and still continues to leverage the sensor data and semantic data of the topology in order to perform consistently as per the shifting environment. With millions of accidents happening due to human error, AVs are a revolutionary concept for mobility in the smart cities or cities of the future. They can contribute significantly in reducing human dependency and avert human errors on the road; and also reduce stress and congestion on roads. Electric AVs will aid in reducing the carbon emissions as well. The introduction of autonomous vehicles will also help in going to the next level and achieving

Vehicle-to-Vehicle communication. Google’s self-driving cars program, Waymo, has recorded the most successful run in the autonomous vehicles category, until now. More is expected in the AV domain in the coming years, something to wait and watch out for.

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Cybersecurity Concerns in the Age of Hybrid Workplaces

Even as the threat of COVID-19 eventually normalizes in our post-pandemic environment, many of the habits and changes we made will likely stay. One of those is hybrid workspaces.

 A hybrid workplace or workspace is a flexible system that allows workers to shift between onsite and offsite work. According to recent data, 65 percent of employees want a hybrid workspace moving forward. This is understandable as working remotely means employees no longer have to deal with the stress and cost of a long commute and can work at their own pace. Supervisors are also embracing the idea of a hybrid workplace because the pandemic proved that employees could be as productive, if not more when working at home.

 It seems like the ideal solution for everyone. However, cybersecurity experts have raised concerns about the hybrid workplace model. 

The risks of remote work

In a traditional office setting, implementing cybersecurity measures such as protection from DDOS attacks is easy. However, in a hybrid workspace, things become a bit more complicated. Most enterprises have a secure network that employee devices can connect to, ensuring some degree of protection. The office devices are also equipped with top-of-the-line antivirus software and are monitored by the I.T. team.

 However, your employees’ home networks and devices may not have this level of security, leaving them vulnerable to potential attacks. Some employees may even be accessing public networks like cafe or library routers, which could jeopardize the company if their device contains sensitive information. Besides this, there’s also the increased risk of employees losing work devices. Some companies provided work laptops or tablets for their employees to bring home. While these devices helped maintain productivity throughout the lockdowns, they are now an additional weak link to the already fragile cybersecurity chain. More persistent cybercriminals now have the option to steal these devices and extract company secrets from them.

 There is also the concern of slower emergency responses. When working onsite, any emergency is quickly made apparent to the supervisors, and the I.T. department as they’re often a few steps away. However, with remote work, you’ll have to call or email to report an incident, and there’s a chance the concerned parties may not be available to address it immediately. This is devastating because even a few seconds can spell the difference between a close call and absolute catastrophe in a crisis like this. 

Cyberattacks are on the rise

During the pandemic, many companies adopted cloud services to facilitate the storage and transfer of data among remote employees. Along with this trend, analysts noticed a 140 percent increase in RDP attacks and a boom in phishing and malware cases. This correlation shows that cybercriminals are aware of the cybersecurity gaps that come with remote and hybrid workspaces and are doing their best to exploit them while companies and experts scramble to find ironclad solutions. 

Securing a hybrid workplace

Unfortunately, no pre-packaged solution can provide a hundred percent guarantee that you won’t fall victim to a cyberattack. However, following the provided steps will at least minimize the risk. 

• Implement strong passwords and activity timers

Whether it’s the device, domain, applications, or other office network service, ensure that strong passwords are in place. Use a mixture of symbols, numbers, uppercase, and lowercase letters. Cybersecurity experts advise never to use the same password and to change it every 60-90 days. In addition, you can improve security by implementing two-factor authentication where you can.

Besides passwords, an additional security measure is implementing activity timers. This will automatically log out a user who has been idle for a certain time. This ensures that users don’t accidentally stay logged into the system and leave it vulnerable to infiltration. 

• Use full disk encryption

Disk encryption ensures that even if a work device were stolen or lost, the information it contains wouldn’t be accessible to hackers. There are various tools available for this purpose, but use one that provides the highest-level security so that even a sophisticated decoding algorithm can’t crack the code. 

• Set access limits

Not all information should be accessible on any remote device by any employee. This ensures some degree of control over the most sensitive company data. Ideally, access to the internal network should only be done on an onsite device monitored by the I.T. department. 

• Educate your employees

Humans are the weakest link in a cybersecurity plan. Even if the system in place is the best current technology has to offer, all it takes is one person’s mistake for it to all come crashing down. Teach your employees the security protocols and the importance of adhering to them. Deliver the information in a way that even those who aren’t tech-savvy will understand. Here are a few key reminders each employee must abide by: 

• Never write down login credentials: It seems obvious, but you’d be surprised how many people keep passwords on post-its, notebooks, or their phones. Understandably, multiple strong passwords are difficult to remember, but use secure password managers instead of writing them down.
• Never connect to public wi-fi on your work devices: There are many risks in connecting to public wi-fi, from hackers intercepting your data to stealing passwords. Even with a VPN, it’s still not recommended.
• Never leave your work device unattended: If your work device is not in use, ensure it is secure, either by keeping it in a locked drawer or room. If you’re bringing it to another location like a library or cafe, never leave it on the table. Some employees have the unfortunate habit of letting their family use their work devices. Even if they don’t have malicious intent, they may unknowingly put the company at risk by clicking on suspicious ads or installing a virus. 

• Partner with cybersecurity experts

Like how you would hire security guards to protect your physical office, it’s best to contract professional-level services to ensure your business’s safety. Most companies were content with basic cybersecurity plans, but if you’re planning to make your workplace thoroughly hybridized, it’s best to upgrade your security to plug all the gaps in remote work. 

Moving forward

While remote work is not new, this is the first time it’s being implemented on such a large scale, and the fact that many companies were not prepared for this situation only puts them even more at risk. There was no time to train employees to conduct remote work without compromising company secrets and no time to prepare the appropriate infrastructure to maintain secure data transfer. 

Fortunately, companies have started investing in tighter cybersecurity measures to complement hybrid workplaces. With this, employees can enjoy greater flexibility without additional risk to the company. In addition, an increased interest in the hybrid workplace means that more funding is being funneled into research focused on strengthening remote security. With these changes, all our worries regarding remote work may soon be a thing of the past.

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Exploring Six React Ecommerce Template Libraries

React is the most popular library for the development of e-commerce applications. React templates for building eCommerce apps are the combination of several components and elements. These small components are packed in containers and then they form the user interface of the React app. React templates for building eCommerce sites act as a blueprint for developers.

React eCommerce templates are dynamic and versatile and they can be used for building an exclusive React app for eCommerce. These templates are completely customizable and can take any shape as you specify them. As the front end of your React app will indicate the quality of your services. It is essential that you should design a scalable system to emancipate your business.

React eCommerce templates significantly improve your speed while React native app development services. You can find dedicated templates that are meant for providing value to your needs. Also, you do not need to make lots of changes to meet your requirements.

Why React Ecommerce Templates?

Ther React library has numerous templates for eCommerce development. While working in such templates you can modify each template according to your need independently. That means you are free to change any element on the UI without affecting other elements. This avoids the need for rendering the entire page every time you modify an element from the interface.

Every template in the react library is comprehensive and can be copied to another template That gives flexibility to a developer. Sometimes creating an interface for eCommerce sites becomes very confusing. In such cases, these templates act as a starting point or inspiration for development.

  Top React Ecommerce Templates

1. Molla

Molla is a fully-featured library for the development of excellent user interfaces and UX. This template library is loaded with a vast set of tools and features from which you can create an interface for the eCommerce app. Also with the help of this template the app developed can have amazing features and performance. This template provides you 20 sample eCommerce sites from which you can take reference for your ideas.

Molla is very convenient for getting a response and has a basic design architecture. It has a simple interface that is quick to understand and operate. It also supports full width strips layouts for the app. Molla provides access to a varied number of icons that are used in the eCommerce business. You can make your react app to display the latest products and services in an interactive manner.

This template can be used in several browsers and can have several animations or transitions for making the app interesting.

2. Novine

Novine is a simplified and interesting library that provides templates for eCommerce apps. Novine has enabled developers to use react.js, Next.js, React-Redux, ES6+, Sass as well as Bootstrap 4. This template library is used for the development of modern eCommerce sites that have excellent responsive capabilities. It has 4 demo react apps to understand the features.

Novine also has support in payment methods with the use of the latest strip methods. The documentation for this template is very detailed and includes everything that this template can do. Also, the components in this template provided by it are easy for modification. In addition to these features, there are a number of functionalities this template can provide you.

The source code of the template is simpler to handle and customize. It has support for a varied number of transitions and animations for every element you add to the app interface.

3. Livani

Livani is a clean and interactive template that is used for making scalable and modern react apps for eCommerce. This template is developed with the utility of Firebase Firestore, Firebase Auth, Express js, etc. it also includes stripe, and express js. Livani template offers a developer all the tools that are required for the development of eCommerce apps. Such apps developed from this template are capable of competing in the growing competition of several industries.

It has more than 5 sample apps, integration to payment methods, and also it is Retina Ready. The most exclusive feature is that the code of the Livani template is SEO optimized. You can also involve multiple fonts through google, interesting animation, and sliders for many actions. This liberty supports sliders and interactive text boxes for providing a responsive layout.

You can get the license of this template with a minimal fee of $ 29.

4. Lezada

With the use of Lezada, you can create extremely sleek and creative eCommerce sites. It is used for multipurpose website designs involving all the features at once in the app. This has all the high-quality features and functionalities that you may require for the Reactjs development services of a scalable eCommerce website. It supports more than 3 headers, 25+ sections ability, and more than 3 footer patterns.

Lezada is designed with the combination of HTML 5, Redux, react, WC3, and many more frameworks. It offers you to operate your website over multiple web browsers without a lack of performance. This is an excellent template for creating a website for product review and description because of the optimized functions of the temples. Lezada creates smart websites that are SEO optimized for the source code.

With all the features and capabilities Lezada is a feature-full template gallery for the development of eCommerce that can generate a majority of engagement.

5. Rick  

Rick is a reactJs template for developing eCommerce apps for mobile devices. This has excellent templates for the development of product selling apps for mobiles. You can use this template to create dynamic apps for selling accessories, digital products, and services. Along with this, the components in this template are made for customization. Hence you can modify the basic structure of the template according to your own requirements.

Rick has support for many google fonts and has cross-platform capabilities. You can create remarkable websites that can grow your business significantly. The structure of the template is very organized so you don’t get confused while making the changes. It too has SEO optimization and no cost updates on the templates. You can purchase the license for using the Rick template for just 24 USD.

 6. Multikart

Multikar is a popular template for designing an eCommerce app with the help of react. It has renowned for its use of creations of online stores for selling various things. This template has special optimization for using the eCommerce app in mobile devices. Also, this template is suggested for new enterprises because the development with their templates is very fast.

The major capability of Multikart is to make payments through Paypal and with other payment methods. It offers an authentication service that protects your website against bots and unauthorized users. If you are developing a large eCommerce app with a number of products this template can be your choice. This has an infinite scroll that can display all your products at once. Multikart supports several currencies.

 Final Verdict 

React templates for eCommerce apps make the job of development very straightforward. They provide the functionalities that can take hours for a developer to design. There is a wide range of tempters available for React that can be used for dedicated projects And the creation of noteworthy eCommerce apps. Mobile apps have become an important part of every business. Mobile apps have been affecting business for quite a while and help in expanding scalability. To develop an astonishing looking app with robust security and modern technology is a tough task. For this QuikieApps, the leading mobile app development company in Bangalore has the best expertise in mobile app development. To develop the finest applications with attractive interfaces and smooth operations, you can count on us.

The advancement of technology has positively influenced the growth of businesses all over the planet. With the help of modern technologies like websites and mobile applications, every firm can sell its products or services online without hassle. We, QuikieApps, have acquired recognition and reputation through the reliance of our respected clients as the top Web development company in Bangalore, India, USA, UK, Dubai. Adapting the dynamic technology of the web and mobile applications is the first step to success in this modish and competitive world.

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How IoT Will Be The Key To A More Personalized And Targeted Marketing

The Internet of things (IoT) is a fancy term for a connected world where almost everything man-made is connected to the internet. This phenomenon is not very full-blown these days. Farms don’t yet have a complete internet-connected irrigation system, and not all cities are laden with geographic sensors. 

But that’s not to say IoT won’t come to fruition. Our voice-assisted technologies like Alexa and Siri have become more personal and responsive in the last five years. Smartwatches get better at examining heart health and providing actionable care. Our voice can jumpstart a host of other mundane appliances like microwaves, TV, and air conditioners. 

While the IoT is not anywhere near full-scale adaptability, its power and importance cannot be understated. For one, tech companies have continually innovated products and services. Hence the industry will grow to more than 1,000 billion USD by 2027. Second, IoT improves the overall efficiency of consumers and the whole community in its continued improvement.

Consumers and cities are not the only ones who would benefit from internet-connected devices. So do marketing and advertising companies. But how? By leveraging the data that all those devices have collected, marketers can provide better content and present customized products and services to their target market. 

Here’s how marketers can benefit from the Internet of Things: 

1. Gather more data 

Let’s say you walked into your kitchen and placed a pre-cooked chicken in the microwave. You turned on the microwave and set the timer through your voice. When you entered your room, you told Alexa, Siri, or Cortana to activate the AC and the laptop and turn off all the lights. 

All these devices generate your data. The length of time you cook your meal, the time you wake up and turn on your AC, and the amount of energy you consume through different appliances. 

The amount of energy they generate, how often you exercise and what day of the week, and what time exactly, how long you leave the house, and what time you’re inside — all these are opportunities for massive amounts of data that no one can previously access. 

In the past decade, all the ways technologies get data is through the available technologies such as laptops, desktops, phones, tablets, and recently smartwatches and earphones. And yes they do good in knowing most about us. They can be nosy, actually. But the data they accumulate are very limited and sometimes not in line with reality. 

IoT enables marketers and other tech companies to look into someone’s daily life. Of course, these should adhere to security and data laws. If done right, marketers and tech companies will learn how consumers interact with the devices, how the devices improve their lives, and what needs improvement. 

So it’s a win-win situation. Again, it’s beneficial to consumers only if the tech companies and marketers handle the data responsibly and in accordance with data protection, laws, and regulations. 

2. Personalized content (better context) 

Imagine you don’t wake up until 11 am. But as early as 7 am, you get ads of slushies and healthy drinks, perhaps advertising companies thinking they could get you to buy morning drinks. Another scenario is when you get bombarded with ads of late-night meals and snacks when you sleep early in the evening. 

These are just a few instances where our current technologies and marketing strategies fall short. Some devices cannot detect what we are presently doing, hence they cannot provide accurate data to marketers. In turn, marketers cannot send customized and personalized content and advertisements for their targeted consumers. 

The Internet of Things and its hoards of connected smart devices, either at home or in the office, have access to data such as daily routines. They know the time you take your lunch or go to school. They know when you’re home when you’re out drinking, or where you’re at the office finishing work. 

Marketing tools can maneuver these beneficial data to both consumers’ and marketers’ advantage. Using the data, marketers can share better advertisements. Likewise, consumers can see personalized content. 

The best part is that both content and advertisements are time and context-sensitive. This means brands reach out to you at the right time and place, leveling up chances of engagement. Let’s accept it. You don’t want to receive ads on lunch when it’s 10 am. IoT data prevent that at all. 

3. Community building

IoT technologies are better community builders. People who use the same wearable device can form specific communities where they both share the benefits and challenges of the devices. 

For example, household X owns an Alexa at home. The kind of content Alexa generates for other people is more likely what’s generated for household X too. And as they get to share content based on these devices, they’ll form communities of like-minded people. 

Marketers can take this as an opportunity to tailor their content to such devices. This is why newer formats such as FAQs and question-like headlines and titles get chosen more than other traditional formats, aka articles. 

Suppose you mostly write long-form articles and not other IoT-optimized formats. In that case, you diminish your chances of getting top results from content generated by IoT devices like Apple watch, Google home devices, factory sensors, or shipping radars. 

So for a marketing strategy to work in IoT, digestible and easy-to-comprehend formats should make part of your creative arsenals. 

In short, IoT devices will make way for new ways of content creation. Ways wherein content are not necessarily in-depth, but more simple, easily understandable, and capable of getting picked up by voice searches. 

4. Conversational commerce

One of the keys to better customer-company relations is through conversational communication. It means when consumers ask, you answer—that simple. Consumers ask for help, you give them the exact support they need. 

For marketers, these need consideration because most of our content is not conversational. Of course, the quality and research is there but the way it is written does not directly answer human queries. IoT and its devices are beginning to change all that. 

Take, for instance, voice assistant devices such as Cortana, Alexa, and Siri. The content they provide is direct answers to human questions. The responses are short and straightforward. And in seconds, they provide the help you actually need. 

Content marketers can learn from this by creating content designed to answer questions or provide help. As long as they are both easy to understand when spoken out loud, chances are your content will make it to the top of those voice-assisted results. 

Specific questions start with why, how, what, and more are good formats to reach the top results. For advertisers, that also means getting past the flowery and inconvenient product description but concise and short words answering some people’s concerns about which your product or service can help. 

Again all this with the goal of having your content reach consumers. And consumers nowadays use voice-assisted AI technologies. If your content is tailored to get picked up by these technologies, you’ll achieve better conversions. 

5. Sustainable and cost-savings

IoT will deliver massive amounts of specific and personalized data. Marketers and big companies can use these data to target an audience that is more likely to buy and use their products and services. 

In this way, there’s no need for A/B testing or targeting a slightly different pool of people to succeed in marketing. With IoT, marketing strategies are laser focus. 

That will translate to a better bottom line. First, when the resources are allocated to specific targets, budgets are lessened but not at the expense of conversions. 

Much more important is that marketing strategies become more sustainable as it hinges on IoT. This marketing ability to transcend hundreds of billions of devices through just the Internet is much cheaper and sustainable. It doesn’t generate loads of electricity, money, and other resources. It only uses what’s widely available on the web and the data provided by the IoT tech producers. 

Final thoughts

AI has already proven itself to be worthy of attention and investment. For companies, It has leveraged the power of branding technologies such as AI logo makers or AI brand tracking. For consumers, it has allowed for a more customized experience. 

But all this can work better if only companies respect personal data privacy. Some companies suggest running data in encrypting technologies. But it may come a long way before everyone adopts such solutions. 

So for the rest of tech companies, it all boils down to responsible handling of data. Or else, the advertising industry will suffer a fatal blow. 

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How AI Is Transforming Marketing for Better Conversions

Even when artificial intelligence (AI) is set to revolutionize the world, it’s clear that not all businesses maximize its potential. In the US, only 9% of companies use machine learning and voice recognition. And of the top 500 US firms, only 29% benefit from AI systems.

All these when the benefits of AI are loud and clear either in terms of monetary value and industry importance. Studies forecast that AI will likely grow to a whopping 17 trillion dollars in 10 years. Tech executives believe AI boosts people to be creative and productive. Plus, it generates more jobs. 

With continued research and innovation, AI will become something that no technology has ever seen. Some say it will become so accurate in predicting that we could control more of the future. Others believe AI will boost us into interstellar travel. While that might be a long shot, today’s AI — a blend of software and digital tools — is already changing the technological landscape. 

Artificial Intelligence as we know it today can mimic human intelligence and give predictive analysis based on billions of past data. And this is good news for almost all businesses. That means you can leverage AI more than human skills, which are prone to error and body limitations. 

Here are some of the best and widely used benefits of AI for businesses of all sizes: 

1. Automates Workflow

To automate and control repetitive, structured, and manual tasks — these are the main purposes of AI. When handled by humans, these tasks are prone to error. Even more, they induce chronic fatigue and restrict creativity among people. 

With AI, it’s possible to control repetitive tasks without human intervention. While AI is doing the work, humans can channel their effort on creativity and leadership work. 

Today’s digital tools are helpful when maneuvering workflow. For example, Timely, Toggl Track, Rescue Time, and Harvest are time-bound AI tools. Which means they help people keep track of time and schedules with ease. 

What’s more, is you can integrate these tools in team settings so that everyone can track time spent on each activity per person. They work in the background, so no one has to do something actively. 

Consider this: if you always take the menial and redundant task of keeping time stamps, chances are it robs you off of the ability to think and be creative. Instead, turn to AI timekeeping software for it does the job. 

Boomerang, Astro, AI Zimov are for those who spend hours on emails. These AI tools help you by reviewing and mimicking your email behavior. They filter messages that need the most immediate replies. Then, they copy your responses from past emails and use the data to respond to less important inboxes. 

For those looking to automate their workflow, AI tools such as Trello are top of the line. Their passive task-tracking ability helps people to break down project schedules and work files. And like Boomerang, these tools review recent behaviors on projects. Because of their machine learning capabilities, one word can trigger many suggestions.

The result: automated workflow prevents employee burnout. The ability to memorize human behavior helps AI tools to act almost independently. This leaves humans more time and energy to work on the creative, collaborative, and happier aspects. 

2. Gathers and Presents Data with Efficiency

Perhaps the most important advantage of AI is its ability to maneuver billions of data. An attribute no human can compare. Businesses nowadays capitalize on its efficiency and speed.

For instance, Deloitte created an AI program that can scan thousands of complicated legal documents. Pulling out and organizing textual information, this AI-powered tool speeds up contracts and other business negotiations.

On the other hand, chatbots are efficient responders. Not only for customer service, AI chatbots help companies distribute satisfaction surveys, collate data, and analyze them. Bots share data to HRs, too: leaves and incentives. Thanks to its analytics, a company could oversee bottlenecks, understaffed or overworked areas, high-cost departments, etc.

3. Automated Branding

Branding gorge on business’ budget. From logo to website design, everything is pricey. Hiring a designer or a design agency is a premium end not all companies can afford. 

But branding tools are getting smarter nowadays. Some logo creator tools such as Zyro, BrandCrowd logo maker, and Themeisle show pre-made logo templates you can customize to suit your brand’s goal image. 

Upon paying for the logo, these sites, for an additional price, provide automatic designs suited for different forms of marketing collaterals such as flyers, business cards, websites, t-shirts, even cups, and mugs. Imagine in a few clicks and cheaper prices, you’ll have a complete brand image. 

Of course, branding runs deeper than visual aspects. It’s the collective experience of all customers toward a business. Analytics tools such as Latana, Adobe Campaign, and Totango help brands feel and listen to customers’ perceptions. 

And that has been made easy with their AI-powered software. This means every transaction leads to analyzing customer behavior, segmenting them, and providing them a better experience next time. All these happen in the background even without human intervention. 

4. Sales Forecasting

The power of AI lies in its predictive technology. And one of the best ways it helps a company is through future forecasts, specifically about sales. 

Let’s accept it. The ultimate goal of business is to get better sales. With the help of AI, companies can calculate the future of sales even for the next few years. They do it by using billions of past data on market situations, brand following, trends, insights, etc. 

And this is insanely helpful for success. Not only can it know whether or not the brand will sell more. AI software provides strategic reports that can also guide the company on its next course of action. 

For example, predictive analytics tools such as those of IBM, SAB, and TIBCO help businesses formulate budgets, allocate resources, estimate potential revenue, and plan future growth. 

Specific uses of these AI tools: provides individual and team sales quotas to hit, a well-established process for salespeople to follow, and detailed customer relationship management (CRM) to track consumers along the sales funnel. 

5. Customer Targeting and Providing Better Algorithms

Social media rampantly use this form of technology. Every user knows this. Say you were searching for the best vlogging camera on Chrome for a set price. Then you log in on your Instagram, and on your feed come a selection of cameras, and this goes on across social media sites like Facebook, Twitter, Tiktok, you name it. which

Today’s social media hoards massive amounts of customers’ data. As a result, some advertising companies and businesses can generate custom-made content for a target audience using these data. 

This technology comprises a big chunk of advertising strategies. You can find these handy tools in CRM platforms, social media analytics, Google Adsense, etc. 

Fortunately, algorithms and customer targeting are not only to hook people to buy. It also helps brands to present unique and customized content for their target audience. For example, Twitter’s and TikTok’s AI gathers previous data so it can suggest things you would most likely engage in. 

Even reputable news sites such as the New York Times and Washington Post use customer-targeting tools. It can generate content based on your past interest. And for non-readers, they present stories that are either advertised or organically posted on their other paid channels. 

So there’s no reason why you shouldn’t adopt Artificial Intelligence. AI’s customer-centric tools are the key to acquiring more customers through targeted advertising strategies or giving more palatable services to your already trusting consumers.

Final Thoughts

AI doesn’t just directly improve a business. One indirect effect, nonetheless significant, is that AI relates to increasing work happiness and satisfaction. You can scour the entire literature on AI benefits, yet none is greater than that of happiness.

Happy people work the hardest. When AI takes over mundane and repetitive tasks, there’s more room for humans to breathe and think. As a result, they get to be more creative and productive, and happy. 

AI may not be in any businesses’ budget. Yet with its tremendous benefits and its projected growth years on, it’s not long before AI penetrates every market.   

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Top Artificial Intelligence Trends for 2021

As a result of the pandemic, the use of artificial intelligence in many businesses has increased. By 2023, according to IDC, investment in AI technology would have increased to $97.9 billion. Artificial intelligence’s potential utility has only increased after the global COVID-19 epidemic. 

AI will become more essential as companies continue to automate day-to-day operations and better comprehend COVID-affected datasets. Businesses are more digitally connected than ever before since the lockdown and work-from-home policy was introduced.

When it comes to identifying the technologies that will revolutionize how we live, work, and play in the near future, AI is undeniably a hot topic. So, here’s a rundown of what we may expect in the coming year as we rebuild our lives and reassess our company plans and objectives.

We’ve witnessed first-hand how critical it is to swiftly evaluate and understand data on viral transmission throughout the world during this current outbreak. Governments, global health organizations, university research institutes, and businesses have joined together to develop new methods for collecting, aggregating, and working with data. We’ve become accustomed to watching the results of this on the news every night when the most recent infection or mortality statistics for our respective regions are announced. Enroll in an AI certification course and grab an AI certification to get started with the journey.

Trends in Artificial Intelligence (AI) to Watch in 2021

The objective of AI adoption is to increase operational efficiency or effectiveness. It can also be used to improve stakeholder satisfaction. Let’s look at the most crucial trends for the year 2021.

AI solutions for IT

AI solutions that can identify typical IT problems on their own and self-correct any minor faults or difficulties are expected to grow in popularity in the coming years. This will decrease downtime and allow teams to work on high-complexity projects while focusing on other things.

AIOps is becoming increasingly popular

The complexity of IT systems has risen in recent years. With AIOps solutions and enhanced analysis of the amounts of data coming their way, IT operations and other teams may improve their critical processes, decision-making, and duties. Forrester recommended IT executives seek for AIOps suppliers who can enable cross-team collaboration through end-to-end digital experiences, data correlation, and toolchain integration.

The data structure will be aided by AI

Organizations will make use of these technologies and generate data that can be used by RPA (robotic process automation) technology to automate transactional activities. RPA is one of the software industry’s fastest-growing segments. Its sole restriction is that it can only work with organized data. Unstructured data may be readily transformed into structured data with the aid of AI, resulting in a specified output.

Artificial intelligence talent will continue to be scarce

The lack of talent is anticipated to be a barrier to artificial intelligence deployment in 2021. There has been a chronic skills vacuum in AI, and businesses have finally recognized its promise. It is critical to close this gap and teach artificial intelligence to a larger number of individuals. In 2021, it will be critical to ensure that a wider range of users has access to artificial intelligence to focus on technology, learning techniques, and enabling a shift in the workplace.

AI is becoming widely adopted in the IT business

The usage of AI in the IT industry has been steadily increasing. On the other hand, some experts believe that businesses will begin to utilize AI in manufacturing and on a huge scale. An organization may achieve real-time ROI with the aid of artificial intelligence. This implies that organizations will reap the benefits of their work.

Augmented Processes have become increasingly popular

When it comes to innovation and automation in 2021, artificial intelligence and data science will be a component of a larger picture. Data ecosystems are scalable, lean, and provide timely data to a wide range of sources. However, in order to adapt and foster innovation, a foundation must be built. Artificial Intelligence may be used to improve software development processes, and we can expect for more collective intelligence and collaboration. To progress toward a long-term delivery strategy, we must cultivate a data-driven culture and go beyond the experimental stage.

Intelligence based on voice and language

The increase of remote working, particularly in customer care centers, has provided a huge potential for NLP and ASR (automated speech recognition) skills to be used. Because one-on-one tutoring isn’t available, businesses may employ artificial intelligence to do frequent quality checks on customer comprehension and intent to assure continuous compliance.

Emotional Artificial Intelligence

Because this technology can perceive, understand, and interact with different human emotions, emotional AI is one of the most popular Artificial Intelligence topics in 2021. Affective computing, as it is sometimes known, takes human-robot communication to a whole new level. Emotional AI can read both vocal and nonverbal signs to comprehend customer behaviour. By analysing how people react to particular topics, products, and services, high-tech cameras and chatbots can readily identify many sorts of human emotions. In the near future, this development in Artificial Intelligence will have a huge impact on the retail business.

Ethical AI

Some well-known businesses, such as Google, Microsoft, Apple, Facebook, and other digital behemoths, are developing ethical AI that adheres to a four-part ethical framework for successful data governance: fairness, accountability, transparency, and explainability. These firms are launching a slew of initiatives and studies in an effort to persuade other businesses to embrace ethical AI that is tailored to their specific needs.

Wrapping up

Over the next 18 months, we may expect more advancements in AI research that will improve our capacity to detect and respond to viral epidemics. This will, however, need continuing worldwide collaboration between governments and private businesses. Global politics and lawmakers, as well as the pace of technical progress, will very certainly influence how this plays out. As a result, concerns like access to medical databases and impediments to international information sharing will be major themes in the next year. artificial intelligence training is on the rise with people slowly understanding the importance and prospects in this industry. Getting an artificial intelligence certification is the sweetest deal in this hour. 

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Business Intelligence: Top Use Cases for the New-Age Businesses

Business intelligence has been making waves all over the world lately, especially in the business side of things. Organizations across all industries have it as a critical component for transformation towards becoming a data-driven enterprise. And, hence it is fueling the need for expanded investments to implement a successful BI strategy with tools, professionals & other training resources required.

Companies can use business intelligence to make a company’s raw data usable. They can help improve decision-making, strategic planning and other business functions. The goal is to make better decisions about your business by utilizing your data in more efficient and effective ways. Because BI has improved so much in the past decade, it’s much easier for more employees across the company to benefit from it. That’s because much of what makes up a business intelligence system is now streamlined or automated.

Are you wondering what that’s all about? Well, here are some of the reasons why it has gained popularity so rapidly among businesses across the broad spectrum of industries.

1. Better customer experiences: The key to success for any given business is its customers. The better you can understand your customers, the better you will be able to serve them and offer top-notch experiences. This, as anyone can tell, results in successful outcomes for the business. To that end, BI helps by providing extensive insights about customers to allow companies to adjust their offerings accordingly and thus deliver quality customer experiences.

2. Enhanced efficiency: Most businesses, no matter the industry they may be a part of, often struggle with efficiency and productivity issues across their operations at some point or the other. Business intelligence can contribute significant value in this regard as well, allowing the company to source data from all systems and analyze it to determine how effectively their processes and employees are performing. For example, in a hospital, it can be used to payroll systems, accounting systems, patient systems, etc. to effectively incentivize staff to achieve better efficiency levels.

3. Marketing: BI allows companies to fine-tune their marketing programs as well. It helps the relevant teams identify which of their campaigns offer the best results, what kind of marketing campaigns tend to work for their industry in particular, which social media platforms their target audience prefers, and countless other such questions and data points. Being able to understand such factors, in turn, empowers companies to better understand customers’ behavior, market trends and thus, adapt their marketing strategies to deliver better results.

4. Customized services: Easily one of the biggest benefits businesses stand to achieve from the use of BI is the ability to deliver personalized services to customers. This is a big win because tailored offerings are the biggest means to garner better sales. So, to help with that, business intelligence allows companies to take a closer look at their customers’ preferences, requirements, market trends, and other factors that are relevant to their industry. Such detailed insights, then, are put to work to develop customized content, products, messaging, etc. that is delivered to customers at the right time to improve chances of conversion and sales.

There is no denying the fact that the world today is brimming with new-age technologies, all of which offer to contribute unique value in some way or another. However, amid this crowd, business intelligence has made a mark. Enabling companies to keep an eye on the latest trends in the market, identify new technologies and important events, streamline their processes across the board, boost operational efficiency, drive better sales, achieve improved results and revenue, etc., business intelligence has quickly proven to be a valuable addition to the arsenal of any business that has had the foresight to embrace it.

What makes it even better is the fact that the benefits are achieved, no matter the industry. So, if you want to achieve all these benefits as well, we recommend you start looking ASAP for an expert vendor for business intelligence services & solutions.

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Orbits of Non-periodic Fourier Series: Simple Introduction, Cool Applications

These Fourier series can be considered as bivariate time series (X(t), Y(t)) where t is the time, X(t) is a weighted sum of cosine terms of arbitrary periods, and Y(t) is the same sum, except that cosine is replaced by sine. The orbit at time t is

where n can be finite or infinite, and Ak, Bk are the coefficients or weights. The shape of the orbit varies greatly depending on the coefficients: it can be periodic, smooth or chaotic, exhibits holes (or not), or fill dense areas of the plane. For instance, if Bk = k – 1, we are dealing with standard Fourier series, and the orbit is periodic. Also, X(t) and Y(t) can be viewed respectively as the real and imaginary part of a function taking values in the complex plane, as in one of the examples discussed here.

The goal of this article is to feature two interesting applications, focusing on exploratory analysis rather than advanced  mathematics, and to provide beautiful visualizations. There is no attempt at categorizing these orbits: this would be the subject of an entire book. Finally, a number of interesting, off-the-beaten-path exercises are provided, ranging from simple to very difficult.

The orbit is always symmetric with respect to the X-axis, since Y(-t) = –Y(t).

1. Application in astronomy

We are interested in the center of gravity (centroid) of n planets P1, …, Pn of various masses, rotating at various speeds, around a star located at the origin (0, 0), in a two-dimensional framework (the ecliptic plane). In this model, celestial bodies are assumed to be points, and gravitational forces between the planets are ignored. Also, for simplification, the orbit of each planet is circular rather than elliptic. Planet Pk has mass Mk, and its orbit is circular with radius Rk. Its rotation period is 2π / Bk. Also, at t = 0, all the planets are aligned on the X-axis.  Let M = M1 + … + Mn. Then the orbit of the centroid has the same formula as above, with Ak = Rk Mk / M for k = 1, …, n.

In the figures below, the left part represents the orbit of the centroid between t = 0 and t = 1,000 while the right part represents the orbit between t = 0 and t = 10,000.

Figure 1

Figure 2

Figure 3

In figure 1, we have n = 100 planets, all the planets have the same mass, Bk = k + 1, and Rk = 1 / (k + 1)^0.7 [ that is, 1 / (k + 1) at power 0.7]. The orbit is periodic because the Bk‘s are integers, though the period involves numerous little loops due to the large number of planets. The periodicity is masked by the thickness of the blue curve, but would be obvious to the naked eye on the right part of figure 1, if we only had 10 planets. I chose 100 planets because it creates a more beautiful, original plot.

Figure 2 is the same as figure 1, except that planet P50 has a mass 100 times bigger than all other planets. You would think that the orbit of the centroid should be close to the orbit of the dominant planet, and thus close to a circle. However this is not the case, and you need a much bigger “outlier planet” to get an orbit (for the centroid) close to a circle.

In figure 3, n = 50, Mk = 1 / SQRT(k+1), Ak = 1.75^(k+1), and Bk = log(k+1). This time, the orbit is non periodic. The area in blue on the right side becomes truly dense when t becomes infinite; it is not a visual effect. Note that in all our examples, there is  hole encompassing the origin. In many other examples (not shown here), there is no hole. Figure 3 is related to our discussion in section 2.

None of the above examples is realistic, as they violate both Kepler’s third law (see here) specifying the periods of the planets given Rk (thus determining Bk), and Titius-Bode law (see here) specifying the distances Rk between the star and its k-th planet. In other words, it applies either to a universe governed by laws other than gravity, or in the early process of planet formation when individual planet orbits are not yet in equilibrium. It would be an easy exercise to input the correct values of Ak and Bk corresponding to the solar system, and see the resulting non periodic orbit for the centroid of the planets.

2. The Riemann Hypothesis

The Riemann hypothesis is one of the most famous unsolved mathematical conjectures. It states that the Riemann Zeta function has no zero in a certain area of the (complex) plane, or in other words, that there is a hole around the origin in its orbit, depending on the parameter s, just like in Figures 1, 2 and 3. Its orbit corresponds to Ak = 1 / k^s, Bk = log k, and n infinite. Unfortunately, the cosine and sine series X(t), Y(t) diverge if s is equal to or less than 1. So in practice, instead of working with the Riemann Zeta function, one works with its sister called the Dirichlet Eta function, replacing X(t) and Y(t) by their alternating version, that is Ak = (-1)^(k+1) / k^s. Then we have convergence in the critical strip 0.5  <  s  <  1. Proving that there is a hole around the origin if 0.5  <  s  <  1 amounts to proving the Riemann Hypothesis. The non periodic orbit in question can be seen in this article as well as in figure 4.

Figure 4

Figure 4 shows the orbit, when n = 1,000. The right part seems to indicate that the orbit eventually fills the hole surrounding the origin, as t becomes large. However this is caused by using only n = 1,000 terms in the cosine and sine series. These series converge very slowly and in a chaotic way. Interestingly, if n = 4, there is a well defined hole, see figure 5. For larger values of n, the hole disappears, but it starts reappearing as n becomes very large, as shown in the left part of figure 4.

Figure 5

If n = 4 (corresponding to three planets in section 1 since the first term is constant here), a well defined hole appears, although it does not encompass the origin (see figure 5). Proving the existence of a non-vanishing hole encompassing the origin, regardless of how large t goes and regardless of s in ]0.5, 1[, when n is infinite, would prove the Riemann hypothesis. 

Note the resemblance between the left parts of figure 3 and 4. This could suggest two possible paths to proving the Riemann Hypothesis:

• Approximating the orbit of figure 4 by a an orbit like that of figure 3, and obtain a bound on the approximation error. If the bound is small enough, it will result in a smaller hole in figure 4, but possibly still large enough to encompass the origin.
• Find a topological mapping between the orbits of figure 3 and 4: one that preserves the existence of the hole, and preserves the fact that the hole encompasses the origin. 

 3. Exercises

Here are a few questions for further exploration. They are related to section 1.

• In section 1, all the planets are aligned when t = 0. Can this still happen again in the future if n = 3? What if n = 4? Assume that the orbit of the centroid is non periodic, and n is the number of planets.
• What are the conditions necessary and sufficient to make the orbit of the centroid non periodic?
• At the initial condition (t = 0), is the centroid always inside the limit domain of oscillations (the right part on each figure, colored in blue)? Or can the orbit permanently drift away from its location at t = 0, depending on the Ak‘s and Bk‘s?
• Find an orbit that has no hole. 
• Make a video, showing the planets moving around the star, as well as the orbital movement of the centroid of the planets. Make it interactive (like an API), allowing the users to input some parameters.
• Can you compute the shape of the hole is n = 3, and prove its existence?
• Try to categorize all possible orbits when n = 3 or n = 4.

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About the author:  Vincent Granville is a data science pioneer, mathematician, book author (Wiley), patent owner, former post-doc at Cambridge University, former VC-funded executive, with 20+ years of corporate experience including CNET, NBC, Visa, Wells Fargo, Microsoft, eBay. Vincent is also self-publisher at DataShaping.com, and founded and co-founded a few start-ups, including one with a successful exit (Data Science Central acquired by Tech Target). He recently opened Paris Restaurant, in Anacortes. You can access Vincent’s articles and books, here.

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