A method of controlling a robot within a volume, the method comprising: receiving a three dimensional model including a model of the robot and a model of the volume in which the robot is configured to move within; defining a plurality of positions within the model of the volume to which the robot is moveable to, the plurality of positions being identified by an operator; receiving scanned three dimensional data of the robot and at least a part of the volume; determining a transformation algorithm using the three dimensional model and the scanned three dimensional data; applying the transformation algorithm to one or more positions of the plurality of positions to provide one or more transformed positions; and controlling movement of the robot using one or more of the transformed positions.

Disclosed is a method of generating a functional singularity at a point or collection of points. The method may include determining a relationship between one or more parameters associated with a physical structure and a spatial gradient of field values of at least one of electromagnetic energy, sound energy, particle beam, or water waves manipulated by the physical structure, configuring, according to the relationship, the spatial gradient of field values to represent a functional singularity at a point, performing backpropagation using the spatial gradient of field values to obtain design parameters corresponding to values for the one or more parameters that achieve the functional singularity at the point, and producing a physical structure having the design parameters.

A usage prediction method executed by a computer, the usage prediction method includes classifying a plurality of records corresponding to a plurality of times included in first time-series data indicating a history of usages of a resource into a plurality of groups respectively corresponding to attributes of the plurality of times; generating second time-series data for each attribute by combining the records belonging to the group corresponding to the same attribute for the plurality of classified groups in order of the times; generating, for each attribute, an expression for calculating a predicted value to be used for calculating a predicted value of the usage based on the generated second time-series data; and calculating the predicted value of the usage based on the expression for calculating the predicted value for each attribute.

A process-implemented neural network method includes obtaining a plurality of kernels and an input feature map; determining a pruning index indicating a weight location where pruning is to be performed commonly within the plurality of kernels; and performing a Winograd-based convolution operation by pruning a weight corresponding to the determined pruning index with respect to each of the plurality of kernels.

Computer processing and outcome prediction systems and methods used to generate algorithm time prediction polynomials, inverse algorithm time prediction polynomials, determine race conditions, determine when a non-linear algorithm can be treated as if it were linear, as well as automatically generate parallel and quantum solutions from classical software or from the relationship between monotonic attribute values.

A decomposition unit (211) decomposes an exponent portion of a final exponentiation computation portion of pairing computation in an elliptic curve into an easy part and a hard part with using a polynomial Φ.sub.k(p(x)), the elliptic curve being expressed by: a polynomial r(x)=Φ.sub.k(T(x))/h.sub.2(x), a polynomial p(x)=h.sub.1(x)r(x)+T(x), and a polynomial t(x)=T(x)+1 which are expressed with using a cyclotomic polynomial Φ.sub.k(x) having a degree d, a polynomial T(x), a polynomial h.sub.1(x), and a polynomial h.sub.2(x); and an embedding degree k. An exponentiation computation unit (22) computes the hard part with using a power of a polynomial p(x).sup.i for each integer i of i=0, . . . , d−1, a power of λ.sub.d−i(x) where λ.sub.d−i(x)=c.sub.d, a power of λ.sub.i where λ.sub.i=T(x)λ.sub.i+1(x)+c.sub.i+1 for each integer i of i=0, . . . , d−2, a power of h.sub.1(x), a power of h.sub.2(x), multiplication, and inverse element computation.

Provided is a technology of optimizing a latent variable by solving a convex optimization problem equivalent to a non-convex optimization problem instead of solving the non-convex optimization problem. A latent variable optimization apparatus includes an optimization unit that calculates an optimum value ˜w* of a latent variable ˜w based on an optimization problem min.sub.˜w(L.sub.convex(˜w)+Σ.sub.d=1.sup.DL.sub.d(˜w)), L.sub.convex being a strongly convex function relevant to the latent variable ˜w, L.sub.d being a function relevant to the latent variable ˜w, S.sub.d,1, . . . , S.sub.d,C being a region that is obtained by dividing a domain of the function L.sub.d into C closed convex sets, ∧.sub.d,c being a convex function that is defined on the region S.sub.d,c and that approximates the function L.sub.d, c.sub.d being a discrete variable that has a value of 1, . . . , C, the optimization unit calculating the optimum value ˜w* by solving an optimization problem min.sub.c_1, . . . , c_D (min.sub.˜w(L.sub.convex (˜w)+Σ.sub.d=1.sup.D∧.sub.d,c_d(˜w))) instead of solving the above optimization problem.

A method of analyzing a vibratory signal derived from rotation of at least one moving part belonging to a rotary mechanism forming all or part of a drive train for transmitting drive torque, the rotary mechanism being fitted to an aircraft and the method comprising at least one first measurement step including measuring vibration in at least one direction and generating a vibratory signal representative of the operation of the rotary mechanism as a function of time, the first measurement step being performed by means of at least one vibration sensor; and at least one second measurement step including measuring an angular position of the moving part, the moving part having at least one degree of freedom to move in rotation about a respective axis of rotation Z. Such an analysis method makes it possible to determine at least one usable range for the vibratory signal.

A decomposition unit (211) decomposes an exponent portion of a final exponentiation computation portion of pairing computation in an elliptic curve into an easy part and a hard part, the elliptic curve being expressed by a polynomial r(x), a polynomial p(x), a polynomial t(x), an embedding degree k, and an integer u. A factorization unit (212) factorizes the hard part with using a homogeneous cyclotomic polynomial Ψ.sub.n(x, p). An exponentiation computation unit (22) performs computation of final exponentiation with using the easy part and the factorized hard part.

Computer processing and outcome prediction systems and methods used to generate algorithm time prediction polynomials, inverse algorithm time prediction polynomials, determine race conditions, determine when a non-linear algorithm can be treated as if it were linear, as well as automatically generate parallel and quantum solutions from classical software or from the relationship between monotonic attribute values.