In fractal geometry, the Higuchi dimension (or Higuchi fractal dimension (HFD)) is an approximate value for the box-counting dimension of the graph of a real-valued function or time series. This value is obtained via an algorithmic approximation so one also talks about the Higuchi method. It has many applications in science and engineering and has been applied to subjects like characterizing primary waves in seismograms, clinical neurophysiology and analyzing changes in the electroencephalogram in Alzheimer's disease. == Formulation of the method == The original formulation of the method is due to T. Higuchi. Given a time series X : { 1 , … , N } → R {\displaystyle X:\{1,\dots ,N\}\to \mathbb {R} } consisting of N {\displaystyle N} data points and a parameter k m a x ≥ 2 {\displaystyle k_{\mathrm {max} }\geq 2} the Higuchi Fractal dimension (HFD) of X {\displaystyle X} is calculated in the following way: For each k ∈ { 1 , … , k m a x } {\displaystyle k\in \{1,\dots ,k_{\mathrm {max} }}\} and m ∈ { 1 , … , k } {\displaystyle m\in \{1,\dots ,k}\} define the length L m ( k ) {\displaystyle L_{m}(k)} by L m ( k ) = N − 1 ⌊ N − m k ⌋ k 2 ∑ i = 1 ⌊ N − m k ⌋ | X N ( m + i k ) − X N ( m + ( i − 1 ) k ) | . {\displaystyle L_{m}(k)={\frac {N-1}{\lfloor {\frac {N-m}{k}}\rfloor k^{2}}}\sum _{i=1}^{\lfloor {\frac {N-m}{k}}\rfloor }|X_{N}(m+ik)-X_{N}(m+(i-1)k)|.} The length L ( k ) {\displaystyle L(k)} is defined by the average value of the k {\displaystyle k} lengths L 1 ( k ) , … , L k ( k ) {\displaystyle L_{1}(k),\dots ,L_{k}(k)} , L ( k ) = 1 k ∑ m = 1 k L m ( k ) . {\displaystyle L(k)={\frac {1}{k}}\sum _{m=1}^{k}L_{m}(k).} The slope of the best-fitting linear function through the data points { ( log 1 k , log L ( k ) ) } {\displaystyle \left\{\left(\log {\frac {1}{k}},\log L(k)\right)\right\}} is defined to be the Higuchi fractal dimension of the time-series X {\displaystyle X} . == Application to functions == For a real-valued function f : [ 0 , 1 ] → R {\displaystyle f:[0,1]\to \mathbb {R} } one can partition the unit interval [ 0 , 1 ] {\displaystyle [0,1]} into N {\displaystyle N} equidistantly intervals [ t j , t j + 1 ) {\displaystyle [t_{j},t_{j+1})} and apply the Higuchi algorithm to the times series X ( j ) = f ( t j ) {\displaystyle X(j)=f(t_{j})} . This results into the Higuchi fractal dimension of the function f {\displaystyle f} . It was shown that in this case the Higuchi method yields an approximation for the box-counting dimension of the graph of f {\displaystyle f} as it follows a geometrical approach (see Liehr & Massopust 2020). == Robustness and stability == Applications to fractional Brownian functions and the Weierstrass function reveal that the Higuchi fractal dimension can be close to the box-dimension. On the other hand, the method can be unstable in the case where the data X ( 1 ) , … , X ( N ) {\displaystyle X(1),\dots ,X(N)} are periodic or if subsets of it lie on a horizontal line (see Liehr & Massopust 2020).
Workplace robotics safety
Workplace robotics safety is an aspect of occupational safety and health when robots are used in the workplace. This includes traditional industrial robots as well as emerging technologies such as drone aircraft and wearable robotic exoskeletons. Types of accidents include collisions, crushing, and injuries from mechanical parts. Hazard controls include physical barriers, good work practices, and proper maintenance. == Background == Many workplace robots are industrial robots used in manufacturing. According to the International Federation of Robotics, 1.7 million new robots are expected to be used in factories between 2017 and 2020. Emerging robot technologies include collaborative robots, personal care robots, construction robots, exoskeletons, autonomous vehicles, and drone aircraft (also known as unmanned aerial vehicles or UAVs). Advances in automation technologies (e.g. fixed robots, collaborative and mobile robots, and exoskeletons) have the potential to improve work conditions but also to introduce workplace hazards in manufacturing workplaces. Fifty-six percent of robot injuries are classified as pinch injuries and 44% of injuries are classified as impact injuries. A 1987 study found that line workers are at the greatest risk, followed by maintenance workers, and programmers. Poor workplace design and human error caused most injuries. Despite the lack of occupational surveillance data on injuries associated specifically with robots, researchers from the US National Institute for Occupational Safety and Health (NIOSH) identified 61 robot-related deaths between 1992 and 2015 using keyword searches of the Bureau of Labor Statistics (BLS) Census of Fatal Occupational Injuries research database (see info from Center for Occupational Robotics Research). Using data from the Bureau of Labor Statistics, NIOSH and its state partners have investigated 4 robot-related fatalities under the Fatality Assessment and Control Evaluation Program. In addition the Occupational Safety and Health Administration (OSHA) has investigated robot-related deaths and injuries, which can be reviewed at OSHA Accident Search page. Injuries and fatalities could increase over time because of the increasing number of collaborative and co-existing robots, powered exoskeletons, and autonomous vehicles into the work environment. Safety standards are being developed by the Robotic Industries Association (RIA) in conjunction with the American National Standards Institute (ANSI). On October 5, 2017, OSHA, NIOSH and RIA signed an alliance to work together to enhance technical expertise, identify and help address potential workplace hazards associated with traditional industrial robots and the emerging technology of human-robot collaboration installations and systems, and help identify needed research to reduce workplace hazards. On October 16 NIOSH launched the Center for Occupational Robotics Research to "provide scientific leadership to guide the development and use of occupational robots that enhance worker safety, health, and well being". So far, the research needs identified by NIOSH and its partners include: tracking and preventing injuries and fatalities, intervention and dissemination strategies to promote safe machine control and maintenance procedures, and on translating effective evidence-based interventions into workplace practice. == Hazards == Many hazards and injuries can result from the use of robots in the workplace. Some robots, notably those in a traditional industrial environment, are fast and powerful. This increases the potential for injury as one swing from a robotic arm, for example, could cause serious bodily harm. There are additional risks when a robot malfunctions or is in need of maintenance. A worker who is working on the robot may be injured because a malfunctioning robot is typically unpredictable. For example, a robotic arm that is part of a car assembly line may experience a jammed motor. A worker who is working to fix the jam may suddenly get hit by the arm the moment it becomes unjammed. Additionally, if a worker is standing in a zone that is overlapping with nearby robotic arms, he or she may get injured by other moving equipment. There are four types of accidents that can occur with robots: impact or collision accidents, crushing and trapping accidents, mechanical part accidents, and other accidents. Impact or collision accidents occur generally from malfunctions and unpredicted changes. Crushing and trapping accidents occur when a part of a worker's body becomes trapped or caught on robotic equipment. Mechanical part accidents can occur when a robot malfunctions and starts to "break down", where the ejection of parts or exposed wire can cause serious injury. Other accidents at just general accidents that occur from working with robots. There are seven sources of hazards that are associated with human interaction with robots and machines: human errors, control errors, unauthorized access, mechanical failures, environmental sources, power systems, and improper installation. Human errors could be anything from one line of incorrect code to a loose bolt on a robotic arm. Many hazards can stem from human-based error. Control errors are intrinsic and are usually not controllable nor predictable. Unauthorized access hazards occur when a person who is not familiar with the area enters the domain of a robot. Mechanical failures can happen at any time, and a faulty unit is usually unpredictable. Environmental sources are things such as electromagnetic or radio interference in the environment that can cause a robot to malfunction. Power systems are pneumatic, hydraulic, or electrical power sources; these power sources can malfunction and cause fires, leaks, or electrical shocks. Improper installation is fairly self-explanatory; a loose bolt or an exposed wire can lead to inherent hazards. === Emerging technologies === Emerging robotic technologies can reduce hazards to workers, but can also introduce new hazards. For example, robotic exoskeletons can be used in construction to reduce load to the spine, improve posture, and reduce fatigue; however, they can also increase chest pressure, limit mobility when moving out of the way of a falling object, and cause balance problems. Unmanned aerial vehicles are being used in the construction industry to do monitoring and inspections of buildings under construction. This reduces the need for humans to be in hazardous locations, but the risk of a UAV collision presents a hazard to workers. For collaborative robots, isolation is not possible. Possible hazard controls include collision avoidance systems, and making the robot less stiff to lessen the impact force. Robotic tech vest is a wearable device for humans, worn in Amazon warehouses. == Hazard controls == There are a few ways to prevent injuries by implementing hazard controls. There can be risk assessments at each of the various stages of a robot's development. Risk assessments can help gather information about a robot's status, how well it is being maintained, and if repairs are needed soon. By being aware of the status of a robot, injuries can be prevented and hazards reduced. Safeguarding devices can be implemented to reduce the risk of injuries. These can include engineering controls such as physical barriers, guard rails, presence-sensing safeguarding devices, etc. Awareness devices are usually used in conjunction with safeguarding devices. They are usually a system of rope or chain barriers with lights, signs, whistles, and horns. Their purpose it to be able to alert workers or personnel of certain dangers. Operator safeguards can also be in place. These usually utilize safeguarding devices to protect the operator and reduce risk of injury. Additionally, when an operator is within close proximity of a robot, the working speed of the robot can be reduced to ensure that the operator is in full control. This can be done by placing the robot in the manual or teach mode. It is also crucial to inform the programmer of the robot of what type of work the robot will be doing, how it will interact with other robots, and how it will work in relation to an operator. Proper maintenance of robotic equipment is also critical in order to reduce hazards. Maintaining a robot insures that it continues to function properly, thereby reducing the risks associated with a malfunction. One common safeguard used in industrial settings is the installation of robot safety fencing. These barriers, often made from durable materials such as mesh or polycarbonate, prevent accidental interactions between workers and robotic systems, reducing the risk of injury. Robot safety fencing is particularly important in environments where high-speed or powerful robots are used. == Regulations == Some existing regulations regarding robots and robotic systems include: ANSI/RIA R15.06 OSHA 29 CFR 1910.333 OSHA 29 CFR 1910.147 ISO 10218 ISO/TS 15066 ISO/DIS 13482
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Moral outsourcing
Moral outsourcing is the placing of responsibility for ethical decision-making onto external entities, often algorithms. The term is often used in discussions of computer science and algorithmic fairness, but it can apply to any situation in which one appeals to outside agents in order to absolve themselves of responsibility for their actions. In this context, moral outsourcing specifically refers to the tendency of society to blame technology, rather than its creators or users, for any harm it may cause. == Definition == The term "moral outsourcing" was first coined by Dr. Rumman Chowdhury, a data scientist concerned with the overlap between artificial intelligence and social issues. Chowdhury used the term to describe looming fears of a so-called “Fourth Industrial Revolution” following the rise of artificial intelligence. Moral outsourcing is often applied by technologists to shrink away from their part in building offensive products. In her TED Talk, Chowdhury gives the example of a creator excusing their work by saying they were simply doing their job. This is a case of moral outsourcing and not taking ownership for the consequences of creation. When it comes to AI, moral outsourcing allows for creators to decide when the machine is human and when it is a computer - shifting the blame and responsibility of moral plights off of the technologists and onto the technology. Conversations around AI and bias and its impacts require accountability to bring change. It is difficult to address these biased systems if their creators use moral outsourcing to avoid taking any responsibility for the issue. One example of moral outsourcing is the anger that is directed at machines for “taking jobs away from humans” rather than companies for employing that technology and jeopardizing jobs in the first place. The term "moral outsourcing" refers to the concept of outsourcing, or enlisting an external operation to complete specific work for another organization. In the case of moral outsourcing, the work of resolving moral dilemmas or making choices according to an ethical code is supposed to be conducted by another entity. == Real-world applications == In the medical field, AI is increasingly involved in decision-making processes about which patients to treat, and how to treat them. The responsibility of the doctor to make informed decisions about what is best for their patients is outsourced to an algorithm. Sympathy is also noted to be an important part of medical practice; an aspect that artificial intelligence, glaringly, is missing. This form of moral outsourcing is a major concern in the medical community. Another field of technology in which moral outsourcing is frequently brought up is autonomous vehicles. California Polytechnic State University professor Keith Abney proposed an example scenario: "Suppose we have some [troublemaking] teenagers, and they see an autonomous vehicle, they drive right at it. They know the autonomous vehicle will swerve off the road and go off a cliff, but should it?" The decision of whether to sacrifice the autonomous vehicle (and any passengers inside) or the vehicle coming at it will be written into the algorithms defining the car's behavior. In the case of moral outsourcing, the responsibility of any damage caused by an accident may be attributed to the autonomous vehicle itself, rather than the creators who wrote the protocol the vehicle will use to "decide" what to do. Moral outsourcing is also used to delegate the consequences of predictive policing algorithms to technology, rather than the creators or the police. There are many ethical concerns with predictive policing due to the fact that it results in the over-policing of low income and minority communities. In the context of moral outsourcing, the positive feedback loop of sending disproportionate police forces into minority communities is attributed to the algorithm and the data being fed into this system--rather than the users and creators of the predictive policing technology. == Outside of technology == === Religion === Moral outsourcing is also commonly seen in appeals to religion to justify discrimination or harm. In his book What It Means to be Moral, sociologist Phil Zuckerman contradicts the popular religious notion that morality comes from God. Religion is oftentimes cited as a foundation for a moral stance without any tangible relation between the religious beliefs and personal stance. In these cases, religious individuals will "outsource" their personal beliefs and opinions by claiming that they are a result of their religious identification. This is seen where religion is cited as a factor for political beliefs, medical beliefs, and in extreme cases an excuse for violence. === Manufacturing === Moral outsourcing can also be seen in the business world in terms of manufacturing goods and avoiding environmental responsibility. Some companies in the United States will move their production process to foreign countries with more relaxed environmental policies to avoid the pollution laws that exist in the US. A study by the Harvard Business Review found that "in countries with tight environmental regulation, companies have 29% lower domestic emissions on average. On the other hand, such a tightening in regulation results in 43% higher emissions abroad." The consequences of higher pollution rates are then attributed to the loose regulations in these countries, rather than on the companies themselves who purposefully moved into these areas to avoid strict pollution policy.
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