Simulation noise is a function that creates a divergence-free vector field. This signal can be used in artistic simulations for the purpose of increasing the perception of extra detail. The function can be calculated in three dimensions by dividing the space into a regular lattice grid. With each edge is associated a random value, indicating a rotational component of material revolving around the edge. By following rotating material into and out of faces, one can quickly sum the flux passing through each face of the lattice. Flux values at lattice faces are then interpolated to create a field value for all positions. Perlin noise is the earliest form of lattice noise, which has become very popular in computer graphics. Perlin Noise is not suited for simulation because it is not divergence-free. Noises based on lattices, such as simulation noise and Perlin noise, are often calculated at different frequencies and summed together to form band-limited fractal signals. Other approaches developed later that use vector calculus identities to produce divergence free fields, such as "Curl-Noise" as suggested by Rook Bridson, and "Divergence-Free Noise" due to Ivan DeWolf. These often require calculation of lattice noise gradients, which sometimes are not readily available. A naive implementation would call a lattice noise function several times to calculate its gradient, resulting in more computation than is strictly necessary. Unlike these noises, simulation noise has a geometric rationale in addition to its mathematical properties. It simulates vortices scattered in space, to produce its pleasing aesthetic. == Curl noise == The vector field is created as follows, for every point (x,y,z) in the space a vector field G is created, every component x, y and z of the vector field (Gx, Gy, Gz) is defined by a 3D perlin or simplex noise function with x, y and z as parameters. The partial derivative of Gx, Gy, and Gz respect to x, y and z is obtained with the gradient of the perlin or simplex noise by finite differences of implicit calculation inside the simplex noise. The partial derivatives are used to calculate F as the curl of G given by F = ( ∂ G z ∂ y − ∂ G y ∂ z , ∂ G x ∂ z − ∂ G z ∂ x , ∂ G y ∂ x − ∂ G x ∂ y ) {\displaystyle F=({\frac {\partial Gz}{\partial y}}-{\frac {\partial Gy}{\partial z}},{\frac {\partial Gx}{\partial z}}-{\frac {\partial Gz}{\partial x}},{\frac {\partial Gy}{\partial x}}-{\frac {\partial Gx}{\partial y}})} == Bitangent noise == This method is based in the fact that the curl of the gradient of scalar field is zero and the identity that expand the divergence of a cross product of two vectors A and B as the difference of the dot products of each vector with the curl of the other: ∇ × ( ∇ φ ) = 0 . {\displaystyle \nabla \times (\nabla \varphi )=\mathbf {0} .} ∇ ⋅ ( A × B ) = ( ∇ × A ) ⋅ B − A ⋅ ( ∇ × B ) {\displaystyle \nabla \cdot (\mathbf {A} \times \mathbf {B} )=\ (\nabla {\times }\mathbf {A} )\cdot \mathbf {B} \,-\,\mathbf {A} \cdot (\nabla {\times }\mathbf {B} )} which means that if the curl of both vector fields is zero then the divergence of the product of two vectors that are the gradients of scalar fields is zero too. This result in a divergence free vector field by construction only calling two noise functions to create the scalar fields. The vector field es created as follows, two scalar fields are calculated ϕ {\displaystyle \phi } and ψ {\displaystyle \psi } using 3D perlin or simplex noise functions, then the gradients A and B of each of this fields is calculated, the cross product of A and B gives a divergence free vector field. == Signed distance noise == The vector field is created based on a closed and differentiable implicit surface S = F(x,y,z) = 0. For every point in the space, frequently outside or near the surface, we get a vector g that is normal to the surface, this is the gradient of S or the partial derivatives respect to x, y and z, this vector is not unitary, but we can get a unitary normal n by dividing each component of the point by the magnitude of the gradient g. Outside of the surface all these normals point away from the surface. g = ∇ F ( x , y , z ) = ( ∂ F ∂ x , ∂ F ∂ y , ∂ F ∂ z ) {\displaystyle g=\nabla F(x,y,z)=\left({\frac {\partial F}{\partial x}},{\frac {\partial F}{\partial y}},{\frac {\partial F}{\partial z}}\right)} n = g ( x , y , z ) ‖ ∇ F ( x , y , z ) ‖ {\displaystyle \mathbf {n} ={\frac {g(x,y,z)}{\|\nabla F(x,y,z)\|}}} ‖ ∇ F ( x , y , z ) ‖ = ( ∂ F ∂ x ) 2 + ( ∂ F ∂ y ) 2 + ( ∂ F ∂ z ) 2 {\displaystyle \|\nabla F(x,y,z)\|={\sqrt {\left({\frac {\partial F}{\partial x}}\right)^{2}+\left({\frac {\partial F}{\partial y}}\right)^{2}+\left({\frac {\partial F}{\partial z}}\right)^{2}}}} Afterwards we calculate a scalar value p for that point in the space using a 3D perlin or simplex noise function. Now we create a vector field V = pn pointing outside of the surface. The curl of this vector field gives the direction in every point in the space where the particles should move. S D N = ( ∂ V z ∂ y − ∂ V y ∂ z , ∂ V x ∂ z − ∂ V z ∂ x , ∂ V y ∂ x − ∂ V x ∂ y ) {\displaystyle SDN=({\frac {\partial Vz}{\partial y}}-{\frac {\partial Vy}{\partial z}},{\frac {\partial Vx}{\partial z}}-{\frac {\partial Vz}{\partial x}},{\frac {\partial Vy}{\partial x}}-{\frac {\partial Vx}{\partial y}})} By construction this vector SDN will point in a tangent direction to an isosurface at the level of the signed distance to the original surface and can be used to confine the movements of the particles to stay in that surface.
Admissible heuristic
In computer science, specifically in algorithms related to pathfinding, a heuristic function is said to be admissible if it never overestimates the cost of reaching the goal, i.e. the cost it estimates to reach the goal is not higher than the lowest possible cost from the current point in the path. In other words, it should act as a lower bound. It is related to the concept of consistent heuristics. While all consistent heuristics are admissible, not all admissible heuristics are consistent. == Search algorithms == An admissible heuristic is used to estimate the cost of reaching the goal state in an informed search algorithm. In order for a heuristic to be admissible to the search problem, the estimated cost must always be lower than or equal to the actual cost of reaching the goal state. The search algorithm uses the admissible heuristic to find an estimated optimal path to the goal state from the current node. For example, in A search the evaluation function (where n {\displaystyle n} is the current node) is: f ( n ) = g ( n ) + h ( n ) {\displaystyle f(n)=g(n)+h(n)} where f ( n ) {\displaystyle f(n)} = the evaluation function. g ( n ) {\displaystyle g(n)} = the cost from the start node to the current node h ( n ) {\displaystyle h(n)} = estimated cost from current node to goal. h ( n ) {\displaystyle h(n)} is calculated using the heuristic function. With a non-admissible heuristic, the A algorithm could overlook the optimal solution to a search problem due to an overestimation in f ( n ) {\displaystyle f(n)} . == Formulation == n {\displaystyle n} is a node h {\displaystyle h} is a heuristic h ( n ) {\displaystyle h(n)} is cost indicated by h {\displaystyle h} to reach a goal from n {\displaystyle n} h ∗ ( n ) {\displaystyle h^{}(n)} is the optimal cost to reach a goal from n {\displaystyle n} h ( n ) {\displaystyle h(n)} is admissible if, ∀ n {\displaystyle \forall n} h ( n ) ≤ h ∗ ( n ) {\displaystyle h(n)\leq h^{}(n)} == Construction == An admissible heuristic can be derived from a relaxed version of the problem, or by information from pattern databases that store exact solutions to subproblems of the problem, or by using inductive learning methods. == Examples == Two different examples of admissible heuristics apply to the fifteen puzzle problem: Hamming distance Manhattan distance The Hamming distance is the total number of misplaced tiles. It is clear that this heuristic is admissible since the total number of moves to order the tiles correctly is at least the number of misplaced tiles (each tile not in place must be moved at least once). The cost (number of moves) to the goal (an ordered puzzle) is at least the Hamming distance of the puzzle. The Manhattan distance of a puzzle is defined as: h ( n ) = ∑ all tiles d i s t a n c e ( tile, correct position ) {\displaystyle h(n)=\sum _{\text{all tiles}}{\mathit {distance}}({\text{tile, correct position}})} Consider the puzzle below in which the player wishes to move each tile such that the numbers are ordered. The Manhattan distance is an admissible heuristic in this case because every tile will have to be moved at least the number of spots in between itself and its correct position. The subscripts show the Manhattan distance for each tile. The total Manhattan distance for the shown puzzle is: h ( n ) = 3 + 1 + 0 + 1 + 2 + 3 + 3 + 4 + 3 + 2 + 4 + 4 + 4 + 1 + 1 = 36 {\displaystyle h(n)=3+1+0+1+2+3+3+4+3+2+4+4+4+1+1=36} == Optimality proof == If an admissible heuristic is used in an algorithm that, per iteration, progresses only the path of lowest evaluation (current cost + heuristic) of several candidate paths, terminates the moment its exploration reaches the goal and, crucially, closes all optimal paths before terminating (something that's possible with A search algorithm if special care isn't taken), then this algorithm can only terminate on an optimal path. To see why, consider the following proof by contradiction: Assume such an algorithm managed to terminate on a path T with a true cost Ttrue greater than the optimal path S with true cost Strue. This means that before terminating, the evaluated cost of T was less than or equal to the evaluated cost of S (or else S would have been picked). Denote these evaluated costs Teval and Seval respectively. The above can be summarized as follows, Strue < Ttrue Teval ≤ Seval If our heuristic is admissible it follows that at this penultimate step Teval = Ttrue because any increase on the true cost by the heuristic on T would be inadmissible and the heuristic cannot be negative. On the other hand, an admissible heuristic would require that Seval ≤ Strue which combined with the above inequalities gives us Teval < Ttrue and more specifically Teval ≠ Ttrue. As Teval and Ttrue cannot be both equal and unequal our assumption must have been false and so it must be impossible to terminate on a more costly than optimal path. As an example, let us say we have costs as follows:(the cost above/below a node is the heuristic, the cost at an edge is the actual cost) 0 10 0 100 0 START ---- O ----- GOAL | | 0| |100 | | O ------- O ------ O 100 1 100 1 100 So clearly we would start off visiting the top middle node, since the expected total cost, i.e. f ( n ) {\displaystyle f(n)} , is 10 + 0 = 10 {\displaystyle 10+0=10} . Then the goal would be a candidate, with f ( n ) {\displaystyle f(n)} equal to 10 + 100 + 0 = 110 {\displaystyle 10+100+0=110} . Then we would clearly pick the bottom nodes one after the other, followed by the updated goal, since they all have f ( n ) {\displaystyle f(n)} lower than the f ( n ) {\displaystyle f(n)} of the current goal, i.e. their f ( n ) {\displaystyle f(n)} is 100 , 101 , 102 , 102 {\displaystyle 100,101,102,102} . So even though the goal was a candidate, we could not pick it because there were still better paths out there. This way, an admissible heuristic can ensure optimality. However, note that although an admissible heuristic can guarantee final optimality, it is not necessarily efficient.
Guideline execution engine
A guideline execution engine is a computer program which can interpret a clinical guideline represented in a computerized format and perform actions towards the user of an electronic medical record. A guideline execution engine needs to communicate with a host clinical information system. Virtual Medical Record (vMR) is one possible interface which can be used. The engine's main function is to manage instances of executed guidelines of individual patients. == Architecture == The following modules are generally needed for any engine: interface to clinical information system new guidelines loading module guideline interpreter module clinical events parser alert/recommendations dispatch == Guideline Interchange Format == The Guideline Interchange Format (GLIF) is a computer representation format for clinical guidelines. Represented guidelines can be executed using a guideline execution engine. The format has several versions as it has been improved. In 2003 GLIF3 was introduced. == Use of third party workflow engine as a guideline execution engine == Some commercial electronic health record systems use a workflow engine to execute clinical guidelines. RetroGuide and HealthFlow are examples of such an approach.
Yale shooting problem
The Yale shooting problem is a conundrum or scenario in formal situational logic on which early logical solutions to the frame problem fail. The name of this problem comes from a scenario proposed by its inventors, Steve Hanks and Drew McDermott, working at Yale University when they proposed it. In this scenario, Fred (later identified as a turkey) is initially alive and a gun is initially unloaded. Loading the gun, waiting for a moment, and then shooting the gun at Fred is expected to kill Fred. However, if inertia is formalized in logic by minimizing the changes in this situation, then it cannot be uniquely proved that Fred is dead after loading, waiting, and shooting. In one solution, Fred indeed dies; in another (also logically correct) solution, the gun becomes mysteriously unloaded and Fred survives. Technically, this scenario is described by two fluents (a fluent is a condition that can change truth value over time): a l i v e {\displaystyle alive} and l o a d e d {\displaystyle loaded} . Initially, the first condition is true and the second is false. Then, the gun is loaded, some time passes, and the gun is fired. Such problems can be formalized in logic by considering four time points 0 {\displaystyle 0} , 1 {\displaystyle 1} , 2 {\displaystyle 2} , and 3 {\displaystyle 3} , and turning every fluent such as a l i v e {\displaystyle alive} into a predicate a l i v e ( t ) {\displaystyle alive(t)} depending on time. A direct formalization of the statement of the Yale shooting problem in logic is the following one: a l i v e ( 0 ) {\displaystyle alive(0)} ¬ l o a d e d ( 0 ) {\displaystyle \neg loaded(0)} t r u e → l o a d e d ( 1 ) {\displaystyle true\rightarrow loaded(1)} l o a d e d ( 2 ) → ¬ a l i v e ( 3 ) {\displaystyle loaded(2)\rightarrow \neg alive(3)} The first two formulae represent the initial state. The third formula formalizes the effect of loading the gun at time 1 {\displaystyle 1} . The fourth formula formalizes the effect of shooting at Fred at time 2 {\displaystyle 2} . This is a simplified formalization in which action names are neglected and the effects of actions are directly specified for the time points in which the actions are executed. See situation calculus for details. The formulae above, while being direct formalizations of the known facts, do not suffice to correctly characterize the domain. Indeed, ¬ a l i v e ( 1 ) {\displaystyle \neg alive(1)} is consistent with all these formulae, although there is no reason to believe that Fred dies before the gun has been shot. The problem is that the formulae above only include the effects of actions, but do not specify that all fluents not changed by the actions remain the same. In other words, a formula a l i v e ( 0 ) ≡ a l i v e ( 1 ) {\displaystyle alive(0)\equiv alive(1)} must be added to formalize the implicit assumption that loading the gun only changes the value of l o a d e d {\displaystyle loaded} and not the value of a l i v e {\displaystyle alive} . The necessity of a large number of formulae stating the obvious fact that conditions do not change unless an action changes them is known as the frame problem. An early solution to the frame problem was based on minimizing the changes. In other words, the scenario is formalized by the formulae above (that specify only the effects of actions) and by the assumption that the changes in the fluents over time are as minimal as possible. The rationale is that the formulae above enforce all effect of actions to take place, while minimization should restrict the changes to exactly those due to the actions. In the Yale shooting scenario, one possible evaluation of the fluents in which the changes are minimized is the following one. This is the expected solution. It contains two fluent changes: l o a d e d {\displaystyle loaded} becomes true at time 1 and a l i v e {\displaystyle alive} becomes false at time 3. The following evaluation also satisfies all formulae above. In this evaluation, there are still two changes only: l o a d e d {\displaystyle loaded} becomes true at time 1 and false at time 2. As a result, this evaluation is considered a valid description of the evolution of the state, although there is no valid reason to explain l o a d e d {\displaystyle loaded} being false at time 2. The fact that minimization of changes leads to wrong solution is the motivation for the introduction of the Yale shooting problem. While the Yale shooting problem has been considered a severe obstacle to the use of logic for formalizing dynamical scenarios, solutions to it have been known since the late 1980s. One solution involves the use of predicate completion in the specification of actions: in this solution, the fact that shooting causes Fred to die is formalized by the preconditions: alive and loaded, and the effect is that alive changes value (since alive was true before, this corresponds to alive becoming false). By turning this implication into an if and only if statement, the effects of shooting are correctly formalized. (Predicate completion is more complicated when there is more than one implication involved.) A solution proposed by Erik Sandewall was to include a new condition of occlusion, which formalizes the “permission to change” for a fluent. The effect of an action that might change a fluent is therefore that the fluent has the new value, and that the occlusion is made (temporarily) true. What is minimized is not the set of changes, but the set of occlusions being true. Another constraint specifying that no fluent changes unless occlusion is true completes this solution. The Yale shooting scenario is also correctly formalized by the Reiter version of the situation calculus, the fluent calculus, and the action description languages. In 2005, the 1985 paper in which the Yale shooting scenario was first described received the AAAI Classic Paper award. In spite of being a solved problem, that example is still sometimes mentioned in recent research papers, where it is used as an illustrative example (e.g., for explaining the syntax of a new logic for reasoning about actions), rather than being presented as a problem.
Catholic Church and artificial intelligence
The Catholic Church views artificial intelligence as a significant technological development that must be governed by strict ethical principles rooted in human dignity and the common good. In January 2025, the Church issued the doctrinal note Antiqua et nova co-issued by the Dicastery for the Doctrine of the Faith and the Dicastery for Culture and Education. It addresses the "relationship between artificial intelligence and human intelligence" and offers reflections on the "anthropological and ethical challenges raised by AI". In August 2025, Time magazine included Pope Leo XIV in its 2025 list of the World’s Most Influential People in Artificial Intelligence. In May 2026, Pope Leo XIV approved the creation of a new Vatican commission on artificial intelligence. He released his first papal encyclical, titled Magnifica humanitas, on the topic later in the month.
NeoPaint
NeoPaint is a raster graphics editor for Windows and MS-DOS. It supports several file formats including JPEG, GIF, BMP, PNG, and TIFF. The developer, NeoSoft, advertises NeoPaint as "being simple enough for use by children while remaining powerful enough for the purposes of advanced image editing". The first version, NeoPaint 1.0, was released in 1992 on floppy disks. It supported video modes ranging from 640x350 to 1024x768 and multiple fonts. NeoPaint 2.2 came out for MS-DOS 3.1 in 1993, with support of for 2, 16, or 256 color images in Hercules, EGA, VGA, and Super VGA modes. NeoPaint 3.1 was released in 1995 supporting 24-bit images and formats like PCX, TIFF and BMP. NeoPaint 3.2 was released in 1996. An updated version, NeoPaint 3.2a, supported the GIF file format. NeoPaint 3.2d was released in 1998. A Windows 95 version named NeoPaint for Windows v4.0 was released in 1999 supporting the PNG file format. On September 1, 2018 the program was rebranded as PixelNEO, becoming one of the VisualNEO software products. Formats such as JPEG 2000, ICO, CUR, PSD and RAW are supported.
David Krueger (professor)
David Krueger is an American machine learning professor and advocate for the reduction of risks related to artificial intelligence. Krueger is an assistant professor in Robust, Reasoning, and Responsible AI at the University of Montreal and a Core Academic Member at Mila. == Early life and education == Krueger obtained a B.A. in mathematics from Reed College, and completed his MSc and Ph.D. in Computer Science at the University of Montreal. He trained in deep learning under Yoshua Bengio, Roland Memisevic, and Aaron Courville from 2013 to 2021. Krueger was also an intern on Google DeepMind's AI Safety team in 2018. == Career == Krueger researches deep learning, AI alignment, and AI safety. His work is focused on reducing the risk of human extinction resulting from out-of-control AI systems. Krueger was an assistant professor at the University of Cambridge from 2021 to 2024, before taking a faculty position at the University of Montreal in 2024. In 2023, he was a founding research director at the UK AI Security Institute. That same year, Krueger initiated the Statement on AI Risk, which argues that AI could cause human extinction and was signed by Anthropic's Dario Amodei, OpenAI's Sam Altman, AI expert Geoffrey Hinton, and other leaders. In April 2026, Krueger discussed the risks of advanced AI at a Capitol Hill event hosted by Senator Bernie Sanders. === Evitable === In 2025, Krueger founded Evitable, a nonprofit organization that advocates for an AI moratorium. == Views == Krueger argues that AI will lead to a "gradual disempowerment" of workers, likening AI chips to nuclear bombs. He also says the military use of AI "poses an existential risk to humanity."