Mesut Kavak
email: kavakmesut@outlook.com.tr

On the Identical Simulation of the Entire Universe

A time ago, I published an article [1] about deceleration of the universe. It was especially based on uncertainty, and it explains how does matter work. In this work, it was performed some analysis of the some specific subjects as an approach such as deceleration, uncertainty, possible particle formation, black hole, gravitation, energy, mass and light speed as the elements for identical simulation computations of the entire universe as the most sensitive as possible being related that article. There are some information about escaping from black holes, event horizon lengths, viscosity of free space, re-derivation of Planck constants [2] and infrastructure of some basic laws of existence mathematically as matter is directly dependent of geometric rules. Also, some elements were given for the readers to solve some required constants as the most sensitive manner. As the constants are not enough in the name of engineering, also finally I found a working algorithm out which reduces process number of the power series to process number of the quadratic equations like calculating a root of an integer as an irrational number by solving equation; so also it can be used to calculate trigonometric values in the best manner for simulations of the entire universe besides physical constants as irrational values.

Introduction

If you want to make a simulation for the entire universe, it means you are in the worst situation; because for example if you must to use π with a number like 10 150 as a multiplier, you must know at least nearly 10 200 digits of π to calculate it for the physical threshold constants which are actually belong to Max Planck. Otherwise, you will be skipped some mass magnitudes which can be create new universes. This is not a acceptable thing in the name of engineering. Also the work does not finish with only π. The Newton's gravitational constant and light speed must be known for the same sensitivity beside actual working principle must be known. Maybe is not true; but I found out Planck constant as an irrational number [START_REF] Kavak | On the Uncertainty Principle[END_REF] as required by uncertainty; but as it is dependent of light speed, also it is assumed that particles draw a perfect circle that is not possible. If we can find out Planck Length or Planck Time and light speed as irrational numbers, then for example we can easily calculate the Newton's gravitational constant in the most sensitive manner without experimental constants that such these experimental constants do not work in such a big simulation if you assume that the simulation is possible.

Universe has been emerging dependent manner of some main physical laws and mathematical rules which are actually natural results for each other. There is nothing inconceivable or unreasonable. Even if there are many laws that universe emerges over them, the most basic law and condition is seen as uncertainty of Werner Heisenberg [START_REF] Heisenberg | The actual content of quantum theoretical kinematics and mechanics[END_REF] as matter owes its availability and process-ability to uncertainty as it has space, formation frequency and formation time differences [START_REF] Kavak | On the Uncertainty Principle[END_REF]. It seems that the deceleration from infinite by a forcing and motion closes a curve as a virtual part of infinite brings energy out at the same ratio by the work done of the forcing work, and because of this simple formation type of matter, as there is no alternative matter sits on some the most basic geometric rules; thus this formation of universe easily will be imitable by computers as there is no difference between real life and a simulation as actually both of them are an illusion because of uncertainty.

During the analysis of the formation process, it can be easily seen that matter's any value is completely irrational as matter is not absolute because of uncertainty as uncertainty increases or decreases between absoluteness and absolute absence but its loss. It always be formed by infinite number of small energies, time differences and side effects on itself. It directly brings irrational values and infinite series out; so if you want to make an identical instant simulation for the entire universe with its future and past, it means you are in the worst situation because of the digits after the comma if you do not want to skip some energy magnitudes that for example maybe these magnitudes can create new universes. Right this point, it is a little relaxing, that even if we could not calculate a identical universe from the basic geometric and mathematical rules except experimental constants, we can use the experimental constants by comparing with the current universal placement which we have by indirect calculations and using induction and deduction methods. By this way, if we achieve the work, even we can learn actual values of the experimental constants which are actually cannot be calculated by experiments since uncertainty is not going to allow this after a point.

Deceleration

As it was said [START_REF] Kavak | On the Uncertainty Principle[END_REF], [START_REF] Kavak | Complement Inferences on Theoretical Physics and Mathematics[END_REF], a matter does work even if it does work relatively to us in outer space observational area by interacting another space elements by using its own energy without external energy source or when made it worked by man-made forcing with external energy, and work can only be done as much as energy existence as kinetic energy is equal to work done. Energy is not independent of velocity, mass, distance and time; thus for creation of a mass, a motion and thus time, distance and velocity must occur without any priority to each other as mass is only possible with existence of energy, and energy is not independent of velocity.

As a motion occurs together with a work by the rule of Figure 1 for y = x and y = x2 functions, a mass cannot get the same mass magnitude at the smaller periods of time as the energy expended for a work which is done to create the mass closes to infinite. Work done is equal to kinetic energy; thus closing to infinite means that even the smallest mass part of universe gains a potential which is able to do infinite work; thus a mass always must get smaller mass magnitude at the smaller periods of time. This means, that work cannot be done untimely manner; thus mass cannot be formed without time, and it cannot be absolute. This is uncertainty as matter is not absolute. It has a emerging frequency. A creation motion always repeats itself, and matter appears in an interval as an illusion.

As matter is not absolute, also there is no absolute threshold value. Any value can get smaller forever, and so there will always emerge infinite time differences for an assumed infinite small mass and energy part of matter. During this appearance between [0, 1] second time interval, as there is no absolute threshold value, also if a mass passes a point on space, its mass effect on just-passed place will never be zero; so there will always be infinite side effects on itself even for just 1 particle which has no other sub particles, or even for the biggest masses have any type atom or particle. Because of this reason, if a particle emerges by a circular motion or a motion which closes a curve of an assumed infinite small mass part as a reference threshold value, it means that there will always be an extra sensed mass. Also again because of this reason, any mass has to be counted as distributed load like snow on ground, and Force = Pressure/Area formula is always in game for any size and magnitude mass. If you use a press machine to compress a material, the material will not be compressed for the same force at a point; because it already will be separated on surface, and so pressure/area ratio will be decreased. You can hole on it by a tip for the same force as actually holing is the same with compressing but you cannot compress it more.

Because of uncertainty, there will always emerge different conditions for different sizes. For example even for the same material, electrical conductivity is different for 1 electron, 1 atom, 1 kg or 1 ton or in heart of stars as a side effect on itself or by external reasons even during emerging duration along 1 second from zero point. For this reason, there is always a probability that we may skip some special effects or behavior. For example we can calculate electron's orbital energy by an experiment if you create a potential difference; but you may not know electron turns around atom like planets or winds a circle or helix on its orbital and also winds this circle own atom on the same orbital at the same time. You always see a cloud as also it is very fast; so you can assume that electron turns like planets. There will no difference for mathematical calculations; but you may be covered some realities also because of some experimental constants like charge de-rived by Coulomb. Math is like a rubber. You can easily make some transformations. Certainly it is not an absolute unknown thing; but maybe we may be wrong. As matter is not absolute, constant speed movement can only be created as it cannot be absolute and is relative [START_REF] Kavak | On the Uncertainty Principle[END_REF], [START_REF] Kavak | Complement Inferences on Theoretical Physics and Mathematics[END_REF]. Energy can only exist in 3 main conditions that they are absolute energy, the energy which is generated by an acceleration from zero point in the other name from nothingness, and the energy caused by an acceleration which is because of a deceleration from any magnitude existent energy the infinite energy is included as well. As matter has no infinite work ability, matter cannot emerge by the acceleration from zero point because of the previous energy need.

As the formation of matter by these rules, as it was said [1] distance taken is dependent of the classic mechanics equations that they are velocity and acceleration equations; thus if it is assumed that d is the distance taken, then they are dependent of d = vt and d = at 2 equation which can be expressed by the other expressions as y = x and y = x 2 functions according to time as the same as on Figure 1. As the intersection point of the functions is x = 1 second, velocity and acceleration increase to the same value at the end of 1 second. Action being the same, the road proceeded during the action performed for the matter which starts to occur after the moment of t = 0 second must be the same road; thus this to be at the same road in 1 ≥ t ≥ 0 time interval condition means that the acceleration decreases from an infinite value as a part of infinite. Deceleration cannot emerge from nothingness because of the previous energy need, and matter can only be created by forcing every second as matter is a virtual part of the infinite as you can neither detract anything from, nor add anything to infinite, since everything an element of the infinite; so it can be said that matter is absolute inert.

As work done is equal to kinetic energy and as matter is created by deceleration, a stopper opposite work on the infinite brings matter total energy out at the amount of this opposite forcing. Also to be one of them before or after of the same two opposite Ft works in space as +Ft and -Ft changes the displacement even momentum and energy will be conserved at that time; so if matter is formed by a circular motion there must be always a potential difference or initial movement for the resultants on Figure 2 to emerge of motion.

Any way, according to the above stated information, we must leave one of the resultants like on Figure 2 to emerge of α α -F +F r Fig. 2: The resultants matter to calculate it. It will be enough for the calculation. Being mvr/r = tan(α), for mvr/r = tan(α) equation it will be as (1) for 1 second.

cos -1 (e -mv ) = α (1)
As required by uncertainty, mass decreases at the same ratio with time [START_REF] Kavak | On the Uncertainty Principle[END_REF] for the smaller slices of time.

Actually, as matter emerges over time, for smaller application time interval than absolute upper time limit which matter gains its maximum mass magnitude value, the mass which the force is applied is smaller than general mass magnitude as the force is smaller as well; so actual equation for this condition is Ft 2 = mtv where t < t u being t u upper limit which means creation time that we accept it as 1 second. Additionally, there is one more option that as motion is deterministic, when you wish to use more energy by the same force by using the force in a smaller time, there will no magnitude difference; thus Ft 2 = mtv becomes invalid. This requires relative time. Time passes different for different motions. Even so, the energy is still used from total energy of universe. If this is the situation, then there are infinite times that is more suitable with uncertainty and the time differences [START_REF] Kavak | Complement Inferences on Theoretical Physics and Mathematics[END_REF], [START_REF] Kavak | On the Uncertainty Principle[END_REF].

Warning

For 2πrα 360 = vt and cos -1 (e -mvt ) = α equations, (1) turns into (2) as the below,

cos -1 (e -πrαm 180 ) = α (2)
and it can only be solved by solving equation as an irrational value, as actually this irrationality is required by uncertainty as well. This angle on (2) is the angle emerges in the smallest time as required by uncertainty as a threshold value. For this angle, the smallest time in the other name the Planck Time can be found out over 2πrα 360 = vt and the smallest distance can be found out over 2πrα 360 as the Planck Length. These ones must be the required Planck constants for example over m = 4π/c 6 , v = c and r = c/2π as they were derived [START_REF] Kavak | On the Uncertainty Principle[END_REF] that is you assume that a creator wave always draws a circle that is impossible [START_REF] Kavak | Complement Inferences on Theoretical Physics and Mathematics[END_REF]. Also when the Planck length is found out over these methods, then the gravitational constant G or the light speed c can be found out on G = L 2 c 7 /4π [START_REF] Kavak | On the Uncertainty Principle[END_REF] being L is the Planck length if also one of them is known as irrational number. Otherwise, we must find out at least one of them as irrational number independent of each other manner; but the Planck time over (2) is not the same with classic one as this is a reference for sensitive calculations. It is about a frequency slip, and explained it the below.

Actually, I found out a different gravitational attraction and repulsion calculation over conservation of momentum of the waves [START_REF] Kavak | Complement Inferences on Theoretical Physics and Mathematics[END_REF] without experimental constant like G.

Warning

If this is the situation then it can be said that Newton's gravitational constant G can be calculated mathematically; but light speed must be known in the same manner as it was said the above. As light speed, Maybe it is a deceleration constant. It may completely mathematical. As universe cannot be absolute even for its any big size, light speed in the other name creation motion speed as required by entanglement must be limited and at least fixed even constant speed movement is not possible as stated the above. Because of the infinite small time differences, the same event is repeated and slowing speed is recovered; so it seems as constant and fixed speed; but as its velocity magnitude, I think it does not increase or decrease. As the first guess about this fixed light speed condition, matter's creation motion and outer space motion emerge and are accepted together [START_REF] Kavak | On the Uncertainty Principle[END_REF], [START_REF] Kavak | Complement Inferences on Theoretical Physics and Mathematics[END_REF]. When it is said that an object moved then it means the circular creation motion moved by using the same space because of the deceleration from the infinite; so you can only say that the object decelerated from A to B if the object moved from A to B. This deceleration constant light speed is as a magnitude of the displacement according to the displacement time, it may always fixed as well as fixed magnitude for any size universe beyond to be fixed because of always limited universe.

Actually, I found out a some methods on possible emergence geometry of particles over conservation of momentum and energy [START_REF] Kavak | Complement Inferences on Theoretical Physics and Mathematics[END_REF]; so actually it is more suitable that we must say a motion closes curve instead of circular motion. A potential difference could not emerge with perfect circular motion.

Warning

As the second guess, matter gains its energy by only a circular motion and if the radius of the motion decreases, then as frequency increased also energy increases for the fixed speed. For the total of universe, when the radius gets smaller during a big bang, then radius of the universe which emerges after the big bang will be bigger because of the bigger centrifugal force and so the energy. Already I derived Planck Constant as 4π/c 4 Js and so if you assume that light speed increased then energy will decrease as a paradox for the first look. This is because of the circular motion frequency. When the frequency increases, then detected mass or energy in an unite of volume increases. Additionally, any time is now and as required by deceleration there can only be one absolute as absolute cannot be created afterwards because of a worker before instead of the created ones; so there cannot be infinite number of universes by a constant velocity even if this velocity is not light speed we know. This is the main reason of why the Planck time which was derived over (2) is not the same with classic Planck time; because even the light speed is fixed, God can force photon to smaller radius by the same speed by using more space volume instead of using little space volume by bigger speed, and then as energy is going to increase also frequency will increase for the same speed and photon energy. At this point, Gravitational constant is the reference to learn how many slip emerged. God created by the rule of [START_REF] Planck | On the Law of Distribution of Energy in the Normal Spectrum[END_REF] or not? This is not an obstacle against finding new planets by calculating universe.

Additionally, maybe light speed can be found out over relative energy transformation [START_REF] Kavak | On the Uncertainty Principle[END_REF], [START_REF] Kavak | Complement Inferences on Theoretical Physics and Mathematics[END_REF]. As I said, the upper limit is for the increasing mass is the total mass of the universe; so if we make an equation like

m ph 1-v 2 c 2 = m u being m ph = 4π/c 6
mass is the photon mass and m u = c 12 /2G 2 mass is the total mass of the universe, then this velocity of v must be the light speed of c. Maybe we can make some corrections even by some series mathematically also by using (7.1) for G and (2) for L and so light speed.

As the deceleration, as it was said the above to emerge of a motion a potential difference is required for the two opposite resultants as matter can only be created by a circular motion. As matter has infinite number of side effect on itself because of infinite number of recovering for speed and so mass and energy as required by uncertainty, for example as any mass increasing increases the drawing mass from the space around it, also this decrease is going to effect the second condition in the other name formed mass's external effect rotation as a side effect by a deceleration which cannot recovered without an external energy. This second external deceleration is different than the creation as space and so matter always want to be fixed from the condition of to be forced creation. Because of this forcing creation condition, any matter wants to stop; but as the forcing is not removed, maximum stopping amount is seen in outer space motion in the other name usual observational space movements as an observational stop. It can be said that outer space moving objects lose their speeds if they rotate around themselves different than the friction with the space induced relative infinite small deceleration. Also this deceleration may cause the famous Bohr Jump in the other name the quantum jump.

As Gravitational constant, I think it is about geometric relation of the light speed. Let us analysis the condition under Viscosity of Free Space title by a new section.

3 Viscosity of Free Space I could not realize exact calculation for the viscosity of free space yet; but I can say, that as required by Newton's third law of motion, physical magnitudes of a space wave is dependent of the density of the space which the wave emerges over it in the point of having different energy magnitudes. Also as the wave has no external energy as it uses for its movement its own total energy, the third law of motion causes energy loss in space for any mass as actually any point of the space is a gravitational field as required by entanglement because of the deceleration from the infinite as there is going to be always different densities, different than assumed zero resistance of the space. There is never going to be an emptiness even if space will be assumed as zero resistance as required by uncertainty as a reference. Also by the way, this condition may cause high pressure area in space by disrupting the vacuum at the total energy amount as particles emerge over the space which is counted as vacuum area; because if you think that there is no other particle in the universe, then if a particle emerges, it stretches the space and the universe will get smaller; so if you create a vacuum area in a tube has no air on the earth, maybe then the temperature does not be like in space because of this.

As required by Newton's third law of motion, as photon is created over space [START_REF] Kavak | On the Uncertainty Principle[END_REF] as a potential difference and wave which has its own energy, it can be said that if free space was denser, photon would be heavier than the previous condition for the same energy. It means that at this condition speed decreases and mass increases for the same energy. If photon was lighter in the same space, then speed would increase instead of it. In the other hand, actually photon's energy is 4π/c 4 Js and its mass is 4π/c 6 Kgs as irrational values as required by uncertainty; so if speed decreases, then it means mass increases by the square of the decrease. This may be the reason of the relation between distance and attraction force; because gravity is the same with formation of a photon. As gravity is photon induced friction in the stretched space as matter can only be formed by photon and a circular motion [START_REF] Kavak | On the Uncertainty Principle[END_REF] this is the same event with a single photon's formation in space.

Actually I discovered, that the actual reason of gravitation is density differences. Denser space is more disordered because you need more speed to create denser area. If you create this denser area over a fixed constant speed, then it is still valid; but even you do not need more speed than the fixed speed, you will converge total energy of the universe for the same speed and after that you will need more speed. During this process, for the creating denser area with a fixed speed, only disorder will increase as long as you create more and more denser area. This is incompressibility of matter. If you create a lower density area, it wants to be fixed by an opposite low force; but if you create denser area, the opposite force will be bigger. Gravity works over this principle. Grav-itational waves frequency is the same an nearly ν = 1 t 0 where t 0 = 3ζ(3) 4πc 3 . Each wave creates a potential difference and when they intersected the space moves according to the condition. As matter emerge over this sliding space, also matter moves. [START_REF] Kavak | Complement Inferences on Theoretical Physics and Mathematics[END_REF] Warning Actually speed cannot decrease and it is for an extraction; but if it was real, the energy of a photon would decrease. This is a paradox for 4π/c 4 Js energy in the point of decreasing energy which is caused by increasing speed; because energy is directly proportional with speed. Then this means that helical circular frequency [START_REF] Kavak | On the Uncertainty Principle[END_REF] increases and detected mass in an unit of volume is preserved. It means that the ratio or the multiplication of frequency (c/2πr) and energy (4π/c 4 ) or frequency (c/2πr) and mass (4π/c 6 ) is fixed constantly as a constant. Now the question is this that by the defined element, how can we extract the gravitational interaction being different than the Newton's?

In the same manner as the second guess, they can be given as the other elements for the gravitational constant that as matter actually draws 3D even if it moves in 2D [START_REF] Kavak | On the Uncertainty Principle[END_REF] because of the circular motion realized around itself of 2D, the mass density can be assumed as in 2D that maybe charge is a mutual matching condition even for any small movement during the rotation of 2D around itself for two particles, and maybe it can cause a cold fusion; so for m 1 /πr 2 mass which is the mass at the distance of r, the other mass which is emerging on this stretched space will be m 1 m /πr 2 as required by Newton's third law of motion as the space is going to be denser because of the other mass. If this is the condition, then because of this 2D total mass against 3D total mass, this multiplication of m 1 m 2 /πr 2 must decrease as the masses is going to get smaller mass magnitudes relatively to each other, and this calculation is going to only be for linear and static condition. Also mass is not only placed at a point even as distributed mass because of the circular motion of matter's creation photon; because as mass density is on the surface [START_REF] Kavak | On the Uncertainty Principle[END_REF], it will move matter forth and back and even if the same two opposite works like +Ft and at the end of the t time -Ft are applied for an object in space, it will change the displacement.

By the way as the third law of motion again, there is going to emerge a subject like vibration stopper densities. Let us analysis the condition in a new section.

Vibration Stopper Densities

As masses lose their energies in a gravitational field and any point of the space is a gravitational field because of the entanglement caused by the deceleration from the infinite as there is not going to be absolute threshold value because of solute matter as gravity effects from infinite distance at the light speed, then space can be assumed as a vibration stopper or reducer density since matter is formed at a frequency. The most extreme densities of the universe are black holes. There is a limit to be a black hole and after this limit, if you do not ask the black hole's life time, any size of black hole can emerge for any radius. In a black hole being h is the Planck constant, ν is the frequency of the photon, m b is the black hole's mass, r b is the black hole's planetary radius, for (3) the below

x 0 (hν/c 2 )m b G (x + r b ) 2 d x = hν (3)
the even horizon's length will be as (4) the below.

x = r 2 b c 2 mG -r b c 2 (4)
As Schwarzschild radius, on (3) when x = 0 meter the Schwarzschild radius will be as (5) the below with zero event horizon length.

r b = m b G c 2 (5)
and also it verifies the kinetic energy correction that as it was said [START_REF] Kavak | On the Uncertainty Principle[END_REF] during motions, because of the creation at the fixed light speed, it can be said that light speed is the highest speed, and the lower is not possible as well. The condition does not allow kinetic energy to be like w = v 0 v d mv ; because the change amount of a mass at low speeds can be assumed as zero, and the speed always must be fixed and the light speed; thus these two conditions do not allow for integration separately even if actually they are the natural results for each other.

According to the work done by gravity, for kinetic energy correction as fixed light speed does not allow for the integration of kinetic energy

m o m b G r 2 b • r b = m o c 2 (6)
the Schwarzschild radius shall be as (6) the above being m o is the object's mass, m b is the black hole's mass, r b is the black hole's planetary radius. As mass has Kgs unit, for any time between [0 -1] second, the work done and the kinetic energy have the same decrease of magnitude in the smaller periods of time; thus for the fixed speed of light and the fixed radius, this surface has the radius of (5) destroys every small string emerging each Planck time because of the space density or tension by reducing and stopping its vibration.

In the same manner, the other black hole [START_REF] Kavak | On the Uncertainty Principle[END_REF] has the radius of (7) as the below

r = mG c (7)
where the gravitational acceleration is equal to the magnitude of the light speed of c, the photon loses its energy at the end of 1 second. By the way, I noticed that the Planck Length which I derived [START_REF] Kavak | On the Uncertainty Principle[END_REF] as (7.1) the below

L = 4πG c 7 (7.1)
*kavakmesut@outlook.com.tr is completely the radius of a black hole as (7) created by a photon has 1 frequency. Also as it was said [START_REF] Kavak | On the Uncertainty Principle[END_REF], If the extra radiation from outside was focused on a particle as a laser beam, since matter can perform action until the extent of its total energy and since vibrations caused by temperature increase will be deemed motion, it would turn matter into photon by vibrating at the emergence frequency about gamma frequency according to the relativistic energy transfer that there is an uncertainty for the speed limit which renders possible v = c on the energy transformation; so the black holes which have this radius (7) may cause gamma ray burst by some periods when the central mass temperature causes a vibration at creation frequency, and the visible light with the gamma rays may be because of decreasing gamma rays caused by the black hole's own dense body. This burst may render visible the black hole as the black hole lose mass and so gravity. Such a dense mass may not let fusion because of mass repel. Photon cannot turn to create particle on dense space after a great density; so you can only see a temperature increase as also the vibration caused by temperature has a shock effect against gravity or electrical charge. If you ask why do the rays travel at two opposite ways, it may occur because of the helical motion.

When ( 5) is used on (4), then the event horizon becomes infinite; but if (7) is used on (4), then an event horizon occurs and it will be as (8) the below, and it starts from the planetary surface.

x = mcG mG - √ mc 3 G (8)
Also because of mv 2 /r force which is gotten by orbital objects light is included as well, escaping is possible even there will be a deformation amount in the escape time; because an uncertainty of the force line condition will emerge as gravity is calculated from the center of objects even for the planetary surface of black holes. For (9.1) the below

m o v 2 r + x ≥ m o m b G (r + x) 2 (9.1)
being r is (7) and x is (4), the equation must always be provided at least for v = c as (9) the below

x ≥ mG c 2 - mG c (9)
and this is an absolute mass repulsion even for light as a hyperbolic perfect mirror. For different x values which are not related with event horizon between [0, x], the repulsion can be seen within different times. By the way, there can be another event similar with this and the deceleration that it can be seen at the outer universe in the other name non-observational universe. As the universe has been emerging by a circular motion and is not absolute, during the photon's emergence over this space, photon which moves linear manner will jump, slide at some points with some periods constantly because of the initial movement as the displacement is going to change; so light cannot come here after a distance. Nothing is perfect because of uncertainty. Also this can be easily the reason of the pioneer anomaly. As space stuff cannot protect their speeds because of the friction with space as a soft collision, also it will turn according to rotation direction of the universe as it emerged by a centrifugal force.

As the Schwarzschild radius destroys the photon's energy for 1 second [START_REF] Kavak | On the Uncertainty Principle[END_REF] without event horizon, if r b = m p G/c 2 Schwarzschild radius is put on its place on (10.1) the below

F 2 = m o m p G r 2 (10.1)
then it will be as (10).

F 1 = m 0 c 4 m p G (10)
This force destroys the energy of the photon in 1 second as it increases the density of the space. If (10) destroys in 1 second, then another interaction for the same planet mass and object with a different radius as F 2 = m o m p G/r 2 destroys in F 1 /F 2 second as required by Newton's the third law of motion as (11).

t p = r 2 c 4 m 2 p G 2 (11)
The same is acceptable for atomic particles and thus all heavenly bodies, and as any point of space is a gravitational field as required by entanglement because of the deceleration from the infinite, any object loses its energy in gravitational field.

Even if there is no other mass in universe, mass loses its energy because of the friction with space being it is a side effect on itself even if the resistance of the space is assumed as zero since it is not actually zero.

As the visible light loss, a visible light loses its energy in gravitational field actually the other photons are included as well, and a dim occurs. If the same energy visible lights suddenly emerge near a planet at the same time, the closer one's loss amount will be more than the further emerging one for the same time; so even if we cannot know all the moves of the universe to determine a certain visible light event horizon, if we can say it started from that place for the visible light, for (12.1) the below

ct 0 h(ν 1 -ν 2 )(r -x) 2 c 4 hν 1 m 2 p G 2 d r = t (12.1)
it will be (12) as

t = Å ν 1 -ν 2 ãÅ r 3 -(r -ct) 3 ã c 4 3ν 1 m 2 p G 2 (12)
by solving equation, and it is a fall from ν 1 frequency to ν 2 , and the visible light event horizon will be (13) as the below

x = r -ct (13)
June 2018 (v.2) being c is the light speed and r is the distance from the center of the planet. The same is acceptable for atomic particles and so all heavenly bodies. You can observe some heavenly bodies like black hole even if the object is not a black hole. Also it can be said that high energy cosmic particles which escaped from a black hole can easily lose their forms and become a different energy particle since gravity sucks energy by space frictions and oneself frictions by superposition of increasing masses. The inner vacuum [START_REF] Kavak | On the Uncertainty Principle[END_REF] area can lose its form like a car tire and maybe it cannot be recovered. Mass spectrometers can be used for the determination of the condition by using the high energy cosmic particles. It may be healer or damager; because for example D 2 O is also water known as heavy water but it is toxic. We should collect high energy particles or the other particles which are created by a big size star or smaller than the earth planet in the space, that they have different energy and vibration.

The Arc Side

It is possible to compute trigonometric functions and π like calculating a root of an integer. It can reduce process number of power series. As the first step, let choosing two points like B and C on Fig. 3, and know that; ∠BAC, the radius and so BC are known. The angle should not be more than 45 • . The other angles between 45 • -90 • will be found out by using half angle formula of cos(2α) = cos 2 (α)sin 2 (α). Otherwise its projection must be drawn for the other side of AB.

Thereupon as the second step, open BC as BC where the radius is the height as the same as on Fig. 4, and lengthen it as 2| BC|. Know that, as | BC| is known, also |BC | and so |AC | are known.

If a circle is drawn for AC radius, then it will look like on Fig. 5, and know that C point is not on EG. The equation becomes Eq. ( 14), If AC radius is intersected with EG by lengthening, and just a part is taken from Fig. 5, it will be as Fig. 6. As ∆GS R and ∆GDE are similar triangles, it will be Eq. (14f).

|AD| = |AE| 3 |AF| 2 (

|GS | |GD|

= |S R| |DE| (14f)
In ∆GS R, as it will be |GR| = |S R| 2 + |GS | 2 also it will be Eq. (14g) over Eq. (14f).

|S R|

= |DE| |HG| • |BE| -|EH| • |DB| |BE| |GD| 2 + |DE| 2 -|DE| • |EH| (14h)
If Eq. (14h) is used on Eq. (14f), it will be as Eq. (14i).

|GS |

= |GD| |HG| • |BE| -|EH| • |DB| |BE| |GD| 2 + |DE| 2 -|DE| • |EH| (
= |AE| 2 + |AG| 2 -|BC | 2 + 2|BC | • |GR| 2|AE| |AG| 2 + |GR| 2 (15)

Area and length relations

If an internal tangent circle is drawn in a square as the same as on Fig. 7, and if length of the square is changed forever gradually, then all the lengths of the circle in the square have to change in the same ratio; because AD is radius of the circle and also |FC| is related with the same radius AF; so also all will be emerged lengths of the circle change at the same amount that; |EF|, |AE|, |DE| and |EB| are included as well naturally. Already it can be analyzed by looking at the radius, ∆ABD and the other chords, the arcs are included as well. It can be said that ratio of two length which are intersected or independent of each other is the same and fixed for changing radius or square sides; so also ratio of the areas which are dependent of the lengths is the same and fixed as well, where lengths and areas are amongst themselves. If this is the condition, then for the circle area A, r radius and square area 4r 2 which emerges for the same radius, it will be a constant like W = 4r 2 /A. Thereupon, let the circle's area is a number like π where r = 1 unit . For this radius, the equation becomes 4r 2 /A = 4/π over the W constant. Finally for changing r values, area of a circle becomes Eq. ( 16).

A = πr 2 (16)

A B

C D E The area of the trapezoid becomes A(DG F C) = (A 2 -A 1 )/2. While r 1 radius is approaching to 0, the area of trapezoid approaches to ∆DG A, and also the area is approaching to a single circle's area with r 2 radius. For the whole circle, it becomes Eq. (16a).

A = lim r 1 →0 π(r 2 -r 1 ) 2 (16a)
Hence it becomes πr 2 for r 2 = r as there is only 1 radius after this. For this condition, after this area of the triangle becomes Cr/2 where C 2 = C for the whole circle. Finally over Cr/2 = πr 2 equation, circumference of a circle becomes Eq. (16b). C = 2πr (16b)

Computation of pi

Relation between area and circumference of a circle is Eq. ( 17)

C = 2A/r ( 17
)
where A is area and C is circumference. If the area is an integer and the angle is an angle like 60 • which has a certain value for cos(60) which can be found out by using an equilateral triangle, then by using Eq. ( 15), r can easily be found out as the circumference is A/3r and the radius is r, by solving equation. By this way, also π can be found out by infinite number of different integer area values for Eq. ( 18)

π = A/r 2 (18)
As the radius after all, if the angle, and the arc which is depended on 2πrα/360 are known on Eq. ( 15), then π directly can be found out for cos(60) and r = 1 as well by solving equation.

Conclusion

Matter is pretty process-able because of uncertainty. It always emerges by forcing and so it is absolute inert. Nothing works. As it was said [START_REF] Kavak | On the Uncertainty Principle[END_REF], matter has an energy potential with a magnitude of mv 2 which has "Joule per second" that can be shorten as (Js) unite for a creation velocity of v because of this availability. As there is no difference for matter if it directly works or made it worked and it is static or moving, we can use matter's own energy without external energy as self-running devices forever to work of it in the name of us each second to its total energy. As we use matter's own energy, it is not so hard to convert energy into force in the other name mass. We can gain more acceleration without external energy source than Jet Fighters without heat and other negativeness. There are some examples [START_REF] Kavak | On the Uncertainty Principle[END_REF], [START_REF] Kavak | Complement Inferences on Theoretical Physics and Mathematics[END_REF].

Also if I am right, we can make an identical simulation of the universe. I found out some physical values of the empty universe approximately such as its mass, volume and radius [START_REF] Kavak | On the Uncertainty Principle[END_REF]; but it is not important; because the important thing is the main functions the each physical phenomena work over them. In theory, there is no difference between real life and a simulation; because both of them are an illusion as well. If we can achieve the work by quantum computers as the main computers, especially it will help astrophysics. Also we will be able to calculate interstellar jumping ship condition in one atom sensitivity. If matter draws more space while it was emerging by using the space, then it can go faster than light when the light speed is fixed at that time. Uncertainty renders this as possible.

If we can achieve the work, also it will help us to find new worlds. We will be able to make a simulation screen that you can see the sky like there is no screen when everything is at its place on sky. We can know any planet's instant weather condition and make a carbon test for a material at the other part of the universe. If we get lost in the universe by teleportation, then we can find where are we at that time by eliminating according to geographical shapes, elements and heavenly bodies around us in theory even if you do not know any physical law, constant and subject by only thinking and using some machines. Even if we cannot find the twin of the universe by these values, we can try it each second for the astrophysical information in our hands as a reference; because even if the gravitational constant is very sensitive, the smallest difference cannot create this universe as the identical twin.

Fig. 1 :

 1 Fig. 1: Deceleration

Fig. 3 :

 3 Fig. 3: Two points on the circumference

Fig. 4 :Fig. 5 :Fig. 6 :

 456 Fig. 4: The arc side

  |GR| = |S R| |GD| 2 + |DE| 2 |DE| (14g) For (|DB|-|S R|)/|BE| = |HR|/|EH| equation over the similarity between ∆RPH and ∆HBE, |HG| = |GR|+|HR| equation turns into Eq. (14h) for |S R|.

  14i) Being the equations are as |GR| = |S R| 2 + |GS | 2 , |ER| = |EG|-|GR|, |AR| = |AG| 2 + |GR| 2 , |BC | = |EG| over the law of cosines for ∠EAC = α, it will be as Eq. (15).

  cosα

Fig. 7 :Fig. 8 :

 78 Fig. 7: Internal tangent circle

Fig. 9 :Fig. 10 :

 910 Fig. 9: The area scanned

2 Deceleration

*kavakmesut@outlook.com.tr

Viscosity of Free Space

Vibration Stopper Densities


Franc ¸ois Alexis Brenon
email: alexis.brenon@imag.fr

Michel Portet

Vacher

Context Feature Learning through Deep Learning for Adaptive Context-Aware Decision Making in the Home

Keywords: smart home, context-aware computing, Ambient Intelligence, reinforcement learning

In Intelligent Environments, prediction and decision must take the context of interaction into account to adapt themselves to the evolving environment. If most of the approaches to deal with this problem have used a formal representation of context, we present in this paper a direct extraction of the context from raw sensor data using deep neural network and reinforcement learning. Experiments undertaken in a voice controlled smart home showed which elements are useful to perform context-aware decision-making in the home and the adequacy of reinforcement learning to tackle an evolving environment.

I. INTRODUCTION

Intelligent Environments, such as smart homes, are fit with numerous sensors and actuators to provide services that enhance users' experience and control over their environment [START_REF] Augusto | Intelligent environments: a manifesto[END_REF]. To make this enriched control possible, these systems perceive their environment and decide which actions to apply to the environment. This decision can be made after some specific events such as a user's request, a scheduled event (e.g., programmed task) or a detected risky situation. This perception is not only useful to trigger a decision but also to adapt the decision making to the current circumstances in which such decision must be performed. These circumstances are called the context and systems that explicitly take the context into account, are said context-aware. However, defining explicitly what pieces of information is playing an important role in the context of a decision is a difficult and tedious task. Indeed, if a general definition of context exists in the field [START_REF] Dey | Understanding and using context[END_REF], the large amount of existing models [START_REF] Bolchini | A data-oriented survey of context models[END_REF], [START_REF] Ibarra | Engineering context-aware systems and applications: A survey[END_REF] demonstrates not only the importance of this notion for research but also the lack of a unified way of modelling context in intelligent environments.

In this paper, we present an approach to perform contextaware decision for voice command in a smart home that does not use an explicitly defined context. Rather, the context information is directly learned from data using deep neural network [START_REF] Schmidhuber | Deep learning in neural networks: An overview[END_REF], [START_REF] Lecun | Deep learning[END_REF]. Indeed, one of the main advantages of Deep Learning (DL) is to learn attributes from raw data at the same time as the classification model is trained. This ability of DL has been demonstrated in numerous classification tasks reaching superhuman accuracy in the case of image classification [START_REF] Lecun | Deep learning[END_REF]. Apart from the identification of necessary elements of the context, another aspect of context awareness is to be able to capture a changing context over time. Indeed, sensors, activity places, dwellers, etc. can change and any system that targets a lifelong support must be able to take these changes into account. To adapt continuously to a changing environment, the decision model we present in this paper uses reinforcement learning to update its decision policy.

The paper is structured as follows. Section II presents the method to represent sensor data for neural network and the reinforced adaptation loop with the decision model acquired using deep learning. A smart home is fit with many heterogeneous sensors that are highly different in term of semantic and dynamic (e.g., temperature, contact-door, speech), thus, this section describes the method used to project this raw information into a unique representation: an image. Moreover, two decision models using different abstraction levels of contextual information are detailed. In Section III, the methods are experimented and compared using a real smart home corpus. The results give an insight of the capability of DL to make decision based on raw data and shed light on the most important contextual information used by the decision model. The approach is then positioned with respect to related work in Section IV before the paper ends with a short conclusion.

II. METHODS

This section presents the adopted data representation (II-A) and the reinforced adaptation loop with the decision model acquired using deep learning (II-B).

A. A common representation for heterogeneous information: a raw image approach

In smart-homes, data are multi-modal: from continuous time series, such as the overall water consumption to event based semantic information such as voice commands or the state change of a device. Hence, finding a representation accommodating low-level continuous values (e.g. water consumption) and high-level categorical events (user current activity) is a problem that has not found a consensual solution in the community. We propose to use a graphical representation, projecting data on a two-dimensional map of the smarthome any time the environment state changes. Then, relevant features from this raw representation are extracted by Convolutional Neural Networks (CNN). This approach provides some advantages: the system sees or understands; 2) Resulting image size is only loosely linked to the number or type of sensors (adding, removing, or changing some sensors will not change the size of the image), hence images accommodate a variable number of data sources (sensors can come and go) a property that classical input vector machine learning approaches do not naturally handle; 3) Image naturally convey spatial information (here an a priory information about the home room organisation); 4) High redundancy of sensor values can be efficiently used by deep learning. Examples of generated images for the smart-home considered in the study are provided in Figures 1 and2 which represent the same situation: the user asks to turn off the radio while she is eating in the kitchen. Black lines represent the walls of the home so that spatial information is provided to the system. To capture context, two representations were chosen. The annotated one, represented Figure 1, uses icons to display humanly annotated contextual information such as location of the user, activity and voice command. In the raw one (Fig. 2), only raw sensor data are represented. For instance usage of light is represented by a black lamp on white background while a turned off lamp is a white lamp on dark background. The highest part presents some gauges for electricity and water consumption while the icon at the bottom left is the uttered command. Images and icons were chosen to maximize the contrast and redundancy for the CNN, to be understandable by human and to be easy to generate on the fly.

B. Decision adaptation through reinforcement learning

The method to continuously adapt the decision model to the situation and the user follows a Reinforcement Learning (RL) strategy. In a RL problem, two components are interacting with each other: the environment and the agent. At each interaction, the agent (here the decision-making system) is fed with the current environment state s t ∈ S. From s t and the past, it chooses an action a t ∈ A to be applied to the environment. The environment (here the house and the user) state is modified by the action (from s t to s t+1 ) and reacts by providing a reward to the agent. This reward R(s t ) = r t can be positive if Fig. 2. Example of generated image from raw data the action is appropriate, negative if the action is not adequate, or null. Based on this reward, the agent adapts its decision policy.

While dynamic programming [START_REF] Bellman | Dynamic Programming[END_REF] can solve the problem of finding the optimal policy, it cannot be used in real settings due to missing information about the environment model and the reward function. Instead, the Q-Learning method [START_REF] Watkins | Learning from delayed rewards[END_REF], can be used to compute and update a policy which will converge toward the optimal one. In Q-Learning, a function, named Qfunction, associates a value, named Q-value, to each possible pair of state-action, named Q-state: Q : S × A → R, where S is the set of possible states of the environment, and A is the set of possible actions to perform. Beginning with an initial Q-function (Q 0 ), it can be updated after each interaction s t , a t , r t , s t+1 , following Equation 1 (where γ is the discounting factor of the reward function and α is a learning rate). This updating rule has been proved to converge toward the actual Q-value of each Q-state, making it possible to compute the optimal policy.

Q k+1 (s t , a t ) = α r t +γmax a Q k (s t+1 , a) +(1-α)Q k (s t , a t )
(1) The learning method is highly dependent on the way the Qfunction is actually represented. For instance, classical implementations choose a tabular representation: a two-dimensional array of Q-values, indexed by states (rows) and by actions (columns). However, this approach does not scale to big or continuous sets of states or actions and does not make it possible to use redundancy in the learning.

Instead of a tabular representation, a deep neural network can be used to approximate the Q-function. In [START_REF] Mnih | Human-level control through deep reinforcement learning[END_REF], a new approach, Deep Q-Network (DQN), has been developed to model the Q-function and applied to a game decision problem given a sequence of video game image frames. Although the work in [START_REF] Mnih | Human-level control through deep reinforcement learning[END_REF] is not the first attempt to use neural network to model the Q-function [START_REF] Tsitsiklis | An analysis if temporal-difference learning with function approximation[END_REF], it is the first which succeeded to implement an efficient learning. Thanks to different optimisation techniques such as the use of a target network, experience replay [START_REF] Lin | Reinforcement learning for robots using neural networks[END_REF], mini-batch learning or RMSProp gradient optimisation [START_REF] Hinton | Lecture 6e -rmsprop: Divide the gradient by a running average of its recent magnitude[END_REF], the learning can converge in reasonable time and is able to scale to large images 1 . This is the approach we adopted and adapted to context aware smart-home decision-making and that is succinctly exposed in the remaining of this section.

The decision model is based on a Convolutional Neural Network (CNN) to process the images followed by a fully connected neural network to compute the Q-value for each action. Figure 3 presents the architecture of our model, the Q-network. The neural network is composed of four convolutional layers, reducing a 256 × 256 input image to features maps of sizes: 16 × 64 × 64, 32 × 21 × 21, 64 × 10 × 10, and 64 × 8 × 8. The features maps of the last layer are then rearranged in a vector of dimension 64 × 8 × 8 = 4096. This vector passes through fully connected linear layers of width 512 and 33 which is the number of possible actions. A rectified linear unit follow each layer except the last one.

Thus, this model provides a way to process the generated images presented in II-A. After preprocessing (scaling and reducing the depth of the image), the image is passed forward in the Q-network. The network builds and extracts relevant features used to compute the Q-value of each possible action. Thus the network can be seen as a the function 33 , where 33 is the number of actions and 256 the size of one side of the image. Then, Equation 1detailed earlier can be used as a loss function to update the weights of the Q-network, as in typical deep learning approaches.

Q -network : [0, 255] 256×256 → R
The overall learning of the decision-making module (the agent) is decomposed into two phases: a pre-training phase (i.e., initialisation of the agent), during which the model is learned from scratch and an adaptation phase during which the model is tuned toward the environment. In practice, the pre-training phase is performed off-line and is mostly devoted to the learning of the CNN and the subsequent neural network. It is well-known that CNN needs a high amount of data ; that is why, in our work, we used artificially generated data to feed the CNN with raw input to learn the CNN weights. In the adaptation phase, the CNN is not supposed to evolve but the last part of the neural network (i.e., the decision part) is biased towards the adaptation data. These data can be either acquired on-line or performed on corpus if available.

In any of these phases, reinforcement learning method is the same. Starting from an initial agent, the system makes maxSteps interactions, in which the observable state of the environment is passed to the agent, before it chooses an action applied back to the environment which releases a reward. All these interactions are recorded by the agent which uses them during a learning procedure. This training epoch (interactions plus training) is realised a number maxEpoch of times.

Since during the pre-training phase the agent explores artificially created data, the environment is not able to evolve consequently to a wrong action. Thus, to multiply the number of situations and explore wrong decisions, up to triesT hreshold actions can be successively tried to simulate the patience of the user, repeating the same command until the system finally behaves correctly. For the pre-training phase, the agent executes a near greedy policy named -greedy policy [START_REF] Sutton | Reinforcement Learning: An Introduction[END_REF]. Given ∈ [0; 1], this policy returns a random action with probability for the action with the highest Q-value given the current state.

To compute the Q-value of each action, the agent uses its approximated Q-function, modelled by the deep neural network Q-Network. However, to ensure a stable learning, the method does not use the latest interaction to compute the error but a set of past interactions from which a (mini-) batch is randomly drawn to train the network. Using this batch, an updated Q-value named target-value is computed and the difference between current Q-values (immediates) and targetvalues (from a set of past interactions) is used as a loss and propagated through the Q-Network [START_REF] Mnih | Human-level control through deep reinforcement learning[END_REF].

III. EXPERIMENTS

The models were trained in two phases: the pre-training phase, where the agent is trained on artificial data and the validation phase which performs a cross-validation on a real corpus. Then, the approach learned from raw sensor data is analysed to explore the kind of sensors and contextual information that are used to make decision. Before entering into the details of the experiment, the input data are presented in the following section.

A. Input data 1) Smart-home Corpus: The dataset used for the validation phase is part of the publicly available Sweet-Home corpus [START_REF] Vacher | The sweet-home speech and multimodal corpus for home automation interaction[END_REF]. It was recorded in the DOMUS smart-home designed by the Laboratoire d'Informatique de Grenoble (LIG) [START_REF] Gallissot | Une plateforme usage pour l'intgration de linformatique ambiante dans l'habitat. l'appartement domus[END_REF]. This 30m 2 home includes a bathroom, a kitchen, a bedroom, and a study as shown in Figure 4. All these rooms are equipped with sensors and actuators such as infrared motion sensors, touch sensors, video cameras (only used for annotation purposes), etc. In addition, seven microphones in the ceiling capture the audio. More than 150 sensors are managed in the flat to provide different services (e.g. light, opening/closing shutters, media management, etc.).

In this study, 15 naïve participants (9 women, 6 men) were recruited to play scenarios of the daily life in the flat. To make the data more natural, the participants were asked to enact the following situations:

• to clean up the flat;

• to prepare and eat a meal;

• to converse via video conference;

• to do leisure activities (reading);

• to take a nap. In each situation, participants were asked to issue a number of voice commands to activate the actuators in the smart home. The objective of this experiment was to test a smart controller in real situations corresponding to voice commands pronounced by the user.

2) State and action sets: A total 11 hours of data of every sensor and actuator were recorded. The smart-home corpus was synchronized and annotated [START_REF] Brenon | Preliminary study of adaptive decision-making system for vocal command in smart home[END_REF]. The annotations consisted in a set of situations, composed of the user's uttered command, the user's location and the user's current activity. This input state is associated to the expected output

C 16 [8 + 2/4] C 32 [6 + 1/3] C 64 [3 + 0/2] C 64 [3 + 0/1] F C 512 F C 33 Q(s, ) Q(s, ) Q(s, ) Q(s, ) Q(s, ) Q(s, )
s Fig. 3. Architecture of the Q-network. s is the input state (image) and Q(s, x) is the Q-value for action x given state s. Cn[f + p/k] denotes a convolution layer (using n filters of size f , with a padding of p, and using a stride of k) and F Cn a fully connected linear layer (of width n). in command type and a location about where to execute the command. For instances, the following excerpt from the dataset shows that a voice command to open the blinds in the kitchen should be followed by the opening of all the blinds of the kitchen. On the second line, when the light is asked to be turned on while cooking in the kitchen, the only possible action is to light on the lamp above the sink. This results in a state space of size 324 = 12 voice commands ×3 locations ×9 activities.

The raw states can take more different possible values. 81 sensors were recorded in the smart home:

• 49 binary sensors;

• 32 continuous sensors which can take values in different ranges (from [0; 100] up to [0; 2 32 -1 = 4294967295]). This leads to more than 10 12 possible states.

From the neural network point of view, a state is an image of size 256 × 256 × 3 pixels, each taking a value between 0 to 255. The resulting state set have a size of 256 256×256×3 = 2 1572864 ≈ 1.75e473479. From which one out of 33 possible actions must be chosen.

3) Generated corpus: Unfortunately, the smart-home corpus does not contain enough relevant samples of voice commands to perform deep-learning from it. As a workaround, a data generation system was developed based on a few generation rules. Two types of corpus were generated: the annotated corpus and the raw corpus. The raw corpus was generated to use the ability of deep learning to build its own features from raw data. The generation consisted in generating annotations for the voice commands and the expected actions as well as simulating values for the raw sensor data. This was performed by producing a random annotated state which is then converted using a set of rules. For example, if the annotated location is the kitchen, then the presence detector sensors of the kitchen are constrained to be active. In the meantime, the bedroom being the room next to the kitchen, its presence detector sensors are constrained to be active with a defined probability. This mechanism is applied for all relevant sensors, while random values are applied to irrelevant ones.

B. Learning results

The two network architectures and image inputs have been trained on artificial data and evaluated on the real Sweet-home corpus. For the DQN with annotated data, the pre-training phase used annotated simulated data composed of annotations about the user's command, location and activity resulting in images with only three icons (Figure 1).

For the DQN with raw sensor data (Figure 2), images were generated during the pre-training phase using a synthetic corpus where all data streams were perfectly synchronized. However, the real smart-home corpus does not provide this quality of synchronization between heterogeneous data streams. To overcome this problem, we chose to provide to the Q-network a wider window of the last 3 seconds of the state of the environment. As a consequence, many samples where no action was required by the agent were introduced (2 samples of no action for any of the 32 other actions), leading to an unbalance dataset biased towards the no action class. To compensate for this learning bias, the reward function was updated so that instead of receiving a reward of (-1), a reward of (-192) is provided if the agent select the no action class when an action is expected.

Once a model is learned from scratch, the evaluation phase adapts it to new data. The Leave One Subject Out Cross-Validation (LOSOCV) method is adopted. This cross validation method keeps one subject file for testing and uses the remaining one for learning, each file in turn. Each fold of the LOSOCV method runs the system for 300, 000 interactions on the real annotated data. Test of the model happens every 6, 000 interactions, running 5, 000 monitored interactions.

A baseline system using a classical tabular Q-learning has been learned and tested by LOSOCV. However, since the classical approach uses a matrix to represent the state, this approach would not be tractable if it was applied directly to the large amount of sensors values (cf. sec II-B). Hence, the baseline was trained on the humanly annotated location and activity labels, which favour the baseline performances.

Table I summarises the result of the learning step. Even though the reinforcement learning objective is to maximise the reward, in this paper, standard classification measures such an F-Measure have been chosen. Indeed, the task can be seen as a classification one, classifying a sample (the environment state) between 33 classes (the actions). In our experiment, a correct classification is considered only when the chosen action is composed of the right action (e.g., turn on) on the right device (e.g., light) at the right place (e.g., study). Any other choice is a wrong classification. While the baseline only deal with humanly annotated data, it presents a low F-Measure of 46%. Regarding the DQN on annotated data the adaptation of the model lead to an average reward of 0.52 and an F-M of 79%. When a DQN is trained and validated on raw sensor data, the score reaches more than 65% of F-Measure. Both DQN approaches demonstrated results far better than the baseline system [START_REF] Brenon | Preliminary study of adaptive decision-making system for vocal command in smart home[END_REF]. The DQN on annotated data exhibits the highest performances but was trained on perfectly humanly annotated high level contextual data (i.e., activity and location) which is not consistent with real usage in which contextual information is inferred and infected with errors. Although, the DQN on raw sensor data does not lead to the best performances, it demonstrates that a context aware decision-making model without an explicit representation of context is possible and lead to a very promising result of 67.5% of F-Measure. An interesting question is to know what kind of information this DQN extracts to make a decision.

C. Analysis of information used by the deep-model

While an associative table can be interpreted for a tabular Q-learning problem, it is more complex to analyse a neural network. This is a recurrent grief addressed to neuronal models, and thus methods have been developed to better understand how they work [START_REF] Karpathy | Cs231n: Convolutional neural networks for visual recognition[END_REF]. We present two complementary analyses. The first one consists in removing some sensor sources in the learning to test their usefulness and the capability of the learning process to overcome the sudden lack of information. The second analysis investigates which features the neural network builds, and if they match the ones usually found in the literature. No PIR No ASR Fig. 5. Learning with a missing information: in blue kitchen motion sensors information (from PIR -Presence Infra-Red -sensors), in green voice command information (from the ASR -Automatic Speech Recognitionsystem).

1) Sensors usage by the deep model: Four experiments were performed, based on a pre-trained (with synthetic raw data) model, in which different kinds of sources of information were removed. As shown on Figure 5, in case of removal of the kitchen motion sensors and during the adaptation phase, the performances are impacted but the system quickly adapts its behaviour to reach back its initial performances. Thus, although this location source is important, the network uses the other available sources to counterbalance this loss of information. Rather, when the speech source is removed, a dramatic fall of the performances appears. However, the same Figure 5 shows that the system still acts with an higher F-Measure (around 20 + -10%) than randomly (a random choice would get about 3% of F-M). This behaviour could be explained by the fact that the system still gets images 2 seconds before an action is expected. This historical information seems to have been used during the pre-training to know when an action is expected. However, the oscillations of the score indicate that the system is not able to infer the user intention only from the sensor values (i.e. from contextual information). The speech signal is thus highly necessary to get user's intention. Two others sensors were removed in the kitchen: the sound detectors and the door switches for kitchen cupboard and fridge. The former are particularly active when the user tidies the home, and one would expect a drop in the performances. But, no impact in the F-Measure performances were noticed while this information is of particular importance for activity recognition.

2) State features: During its forward pass through the network, the input image is transformed to extract relevant features, resulting in high-dimensional vectors. One way to study these vectors is to project them in a two-dimensional space while preserving some inter-vectors relations such as the euclidean distance. One of the most used projection methods is the t-SNE (t-distributed Stochastic Neighbour Embedding) projection [START_REF] Van Der Maaten | Visualizing high-dimensional data using t-sne[END_REF] which performs very well to project vectors issued by a convolutional neural network. In the following experiment, we provide some states (images) to a pre-trained model, while recording vectors after the last convolutional layer, and the one before the last fully connected layer. These vectors are also linked to the information characterising the input state (location, activity, uttered command, expected action, sensors activity). Projecting the vectors provide a bi-dimensional coordinate (0, 0) ≤ (x, y) ≤ (1, 1) able to represent any of the linked information.

Results presented in Figures 6 and8 show that some information is identified and extracted by the convolutional part of the network. For example, the network projects input data into blobs that are coherent both with respect to the users' location (colored area in Fig. 6) and with respect to uttered commands (colored area in Fig. 8). By contrast, no group are spotted for human activities (Figure 7). On the zoomed zone very different activities such as do nothing (the cross), eating (crossed knife and spoon) and cooking (oven) are projected in the same area. These results confirm the interest of user location as a contextual information but user activity does not seem to be a relevant feature for the neural network to estimate decision. However, if semantic labelling of the activity is not exploited by the network, more low-level activity measures, such as agitation level, could be studied.

The last projection, presented in 9, provides information about the way the neural network transforms the space to make each class linearly separable. While there is a majority of Do Nothing action, we can identify some groups of common action type (icon type) and action place (icon colour), proving that images of state contain enough information to decide which decision to make.

IV. RELATED WORKS

Typical smart-homes considered in the study are the ones that permit voice based interaction. This kind of smart homes is particularly suitable to people in loss of autonomy [START_REF] Portet | Design and evaluation of a smart home voice interface for the elderly: acceptability and objection aspects[END_REF], [START_REF] Vacher | Evaluation of a context-aware voice interface for ambient assisted living[END_REF]. Although it recently gained interest in the speech processing community [START_REF] Istrate | Embedded implementation of distress situation identification through sound analysis[END_REF]- [START_REF] Barker | Multi-microphone speech recognition in everyday environments[END_REF] none of these work formalises the voice command recognition as a context-aware decision problem. In that case, identifying what contextual information is needed to understand the intention of the user for it utterance is of particular importance.

Regarding contextual information and context extraction, research on context aware systems has generated a vast amount of knowledge representations. The main trend for knowledge representation in smart environments has become ontology, in particular those based on Description Logic [START_REF] Rodríguez | A survey on ontologies for human behavior recognition[END_REF], [START_REF] Liao | A rdf and owl-based temporal context reasoning model for smart home[END_REF]. This approach is also popular to model the current context for mobile applications [START_REF] Attard | Ontology-based situation recognition for context-aware systems[END_REF], [START_REF] Yilmaz | iConAwa an intelligent context-aware system[END_REF]. However, Description Logic has not been originally designed to model imprecision in sensors data or inferences that is why extension with fuzzy representation had been proposed [START_REF] Rodríguez | A fuzzy ontology for semantic modelling and recognition of human behaviour[END_REF]. Another important contribution to make ontologies capable of dealing with uncertainty is the use of probabilistic models in ontology inference. A notable application of such approach has been presented by [START_REF] Helaoui | A probabilistic ontological framework for the recognition of multilevel human activities[END_REF] and by [START_REF] Chahuara | On-line human activity recognition from audio and home automation sensors: comparison of sequential and non-sequential models in realistic smart homes[END_REF].

In all of these approaches, the context modelling is considered from a top-down perspective, where elements of the context are identified by expertise. In this paper, we propose a different approach: a data-driven constitution of the context where all the sensor data are unified into a common representation: an image. The closest work to this approach is the recent one by [START_REF] Singh | Transforming sensor data to the image domain for deep learning -an application to footstep detection[END_REF] which transforms pressure sensor data into image domain to perform gait identification. In this work, a pressure sensor matrix is converted into an image to perform CNN and RNN learning. However, in their work the data were already sequences of 2-dimensional values while in our case we dealt with a set of monodimensional sensor data of variable type (Boolean, categorical, numerical) projected in the schema of the home. Our approach is thus more adapted to context-awarness in smart home and provide the user with an understandable data representation.

Regarding the decision-making process, several logic-based approaches are presented in the literature using description logic [START_REF] Kofler | A semantic representation of energy-related information in future smart homes[END_REF], [START_REF] Gómez-Romero | Context-based scene recognition from visual data in smart homes: an information fusion approach[END_REF] or fuzzy logic [START_REF] Moore | Rule strategies for intelligent context-aware systems: The application of conditional relationships in decision-support[END_REF]. However, in these proposals the system is set a priori to execute an action given a specific configuration (the condition) and consequently the system does not adapt its behaviour to a changing situation. Some research work on context aware systems have relied on Bayesian Network [START_REF] Mitra | A probabilistic context-aware approach for quality of experience measurement in pervasive systems[END_REF]- [START_REF] Carolis | C@sa: Intelligent home control and simulation[END_REF] or Markov Logic Network [START_REF] Chahuara | Context-aware decision making under uncertainty for voice-based control of smart home[END_REF] which brings the advantage of being learned from data. However, these approaches do not include mechanism to adapt the decision model to new situations. Furthermore, if part of the model can be learned from data, the logic part is acquired by human expertise which has the same drawback as the logic based knowledge representations in smart-home.

To tackle the problem of adaptation, some researches in smart-home have designed the decision problem as a reinforced decision-making problem. One of the most famous of these works is The Neural Network House [START_REF] Mozer | The neural network house: An environment that adapts to its inhabitants[END_REF] where a smart home was controlled by the ACHE system [START_REF]Smart Environments: Technology, Protocols and Applications[END_REF], which commanded the lights in order to reduce the overall energy consumption without impairing the inhabitant comfort based on the perceived environment. Although this project showed promising results and gave rise to other research [START_REF] Zaidenberg | Reinforcement learning of user preferences for a ubiquitous personal assistant[END_REF], [START_REF] Hassan | Action prediction in smart home based on reinforcement learning[END_REF], the RL technique employed poorly scales to large real cases sets. As demonstrated in [START_REF] Mnih | Human-level control through deep reinforcement learning[END_REF], a way to solve this issue, is to change the data structure, relying for example on a deep neural network [START_REF] Schmidhuber | Deep learning in neural networks: An overview[END_REF], [START_REF] Lecun | Deep learning[END_REF]. Following the work of [START_REF] Mnih | Human-level control through deep reinforcement learning[END_REF] who proposed deep reinforcement learning called Deep Q-Network (DQN), we adapted this approach for the first time to the smart home domain and used it to exhibits the kind of context information that is useful for adaptive decision-making.

V. CONCLUSION

The results of the experiments of a reinforcement learning method with a deep model for automatic adaptive decisionmaking in smart-homes show promises. In particular, the experiments show that:

• the deep model can learn the relevant contextual information from raw data; • the system can adapt its model to an evolving set of sensors; • graphical representation of smart-home multi-modal heterogeneous data can be interpreted by the system to make correct decisions; • the method can scale from small input spaces (annotated data) to big input space (raw sensor data). Despite the model learned from raw data shows a slightly weaker F-Measure than the one learn from annotated highlevel contextual input, this former model make it possible to do without specialised external inference models. Indeed, in typical settings, user's location, activity and decision are processed independently to form a processing pipeline. While this approach has its own virtue by making the information formally defined and shareable, this processing chain must deal with the uncertainty propagated along the pipeline and the difficulty of adapting the whole chain to changes in the smarthome. With a deep model and reinforcement learning, the context is automatically learned and tuned toward the decision task and is thus more robust to change in the home.

However, Deep Learning is very demanding in training data and computation time. For instance, in the raw data settings, it took about 8000000 interactions (which correspond to 100 days in real time) before the system acquires a coherent behaviour. It took more than 4 days and 16 hours to compute this experiment on the recorded corpus. While the learning is far too long for a home, we have shown that using artificially created data, this learning phase can be subsequently adapted to new data in a time comparable to tabular Q-learning [START_REF] Brenon | Preliminary study of adaptive decision-making system for vocal command in smart home[END_REF].

In conclusion, Deep Learning generates great expectations given its success in many tasks in data processing and reasoning. But, beyond the shift in performance, what is probably the most interesting from a scientific perspective is its ability to learn features from raw data to inform us about which information comes into play when solving a problem such as context-aware decision-making. Although the model used in this study (neural network) does not reach the level of expressiveness of logic based approach, its ability to extract features from raw data can play a role in defining what the most important context elements might be in intelligent environment applications.

Fig. 1 .

 1 Fig. 1. Example of generated image from annotations

Fig. 4 .

 4 Fig. 4. The Domus smart-home

  blind -open kitchen none -> blind -open kitchen light -on kitchen cook -> light -on kitchen -sink

Fig. 6 .

 6 Fig. 6. Post-convolution t-SNE projections: User location

Fig. 8 .

 8 Fig. 8. Post-convolution t-SNE projections: Uttered command

Due to space constraint the reader is refereed to Mnih et al.[START_REF] Mnih | Human-level control through deep reinforcement learning[END_REF] for details.