Isothermal brain predicting Mcculloch-Pitts logic implicating Walter freeman ionic diffusion and Lotfi Zadeh fuzzy logic that might be useful for coding autonomous vehicles to be coexisting with the pedestrians

We wish to demonstrate mathematically a possibility of fuzzy thinking in homo sapiens. We begin with the fundamental physiological fact that human brains are kept at a constant temperature, we can prove McCulloch-Pitts sigmoid-σ formula adopted by Artificial Neural Networks (ANN) as neuronal firing rates. Then, we verify sigmoid-σ to be the exact solution of nonlinear Riccati differential equation (Jacopo Riccati, 1676–1754). Furthermore, applying the baker transform of Riccati equation we derive the Einstein thermal diffusion equation governing neuron’s transmitting ion’s dynamics in the propagation wave front. Given the aforementioned background, we review the neurophysiology that the most abundant cells in our brains are glia (Greek: glue), which are ten time smaller but ten times more abundant than the mm-size neurons. Their functionalities are more than passive house-keeping cleaning brain debris at the nights avoiding dementia Alzheimer disease, but also actively modulate the ion diffusion firing rates during the days. Especially, the glia cells generate a derivative of cholesterol fatty acids known as Myelin sheath coating of the Axon to keep Calcium ionic current within, without being short circuit with the other causing Epileptic seizures. The insulation is sausage-like modulation from the root reservoir Axon Hillock all the way to reach the other neuron’s Dendrite Tree. The longest Axon is over a meter long from the head to the toe. While one ion is push inward from the Axon Hillock, the other end ion will be out to the Dendrite in a real time. That’s how we issue the command to run away from predators, e.g. Tiger, or chase after preys. A temporary pile up of Calcium ions at the Axon Hillock is possible in the sense of increasing the concentration in backward propagation. This temporarily out of the normal order of forward propagation might be responsible for the bifurcation leading to chaotic dynamics of Walter Freeman, as well as the envelope of bifurcation maps becomes Lotfi Zadeh fuzzy membership function. We


Introduction
Takeshi Yamakawa has successfully applied fuzzy logic to consumer electronics and made the sale in Japan, because the word "fuzzy" sounds like the famous "Fuji" mountain in Japan. For example, Japan has fuzzy air conditioning, fuzzy coffee pot, fuzzy cloth washer, fuzzy automatic transmission, except fuzzy camera which might not sell in the World. When the 3 rd Gen AI has incorporated the Lotfi Zade's fuzzy membership functions (FMF) capturing vehicle dynamics, and pedestrian emotional responses, we believe Autonomous Vehicle (AV) called fuzzy Toyota may take off. We refer to Google-developed Alpha Go Artificial Intelligence (AI) as the 2 nd Gen AI that Google applies artificial neural network (ANN) to learn the 'If: Then' rules as ANN's I/O. The 1 st Gen AI is a fixed Rule-Based System proposed by Marvin Minsky of MIT circa 1990. The 2 nd Gen AI can beat human on the Go-Chess Game in 2015. Yet, possibility thinking. We sometimes violate sensibly the traffic rule during a red traffic light when a human driver will take a right hand turn yielding pedestrians & cars. However, AV cannot do that. This might be due to the automation computer scientists have not digitally captured the human emotional intelligence and program multi-level fuzzy logic in thinking. When this is digitally done successfully, the 3 rd Gen AI machine can exit with human being peacefully.
The Myelin sheath that is the fatty acids protein generated by glia cells to separate and speed the transmission of ion current and protects it from short-circuiting from another cell, e.g. causing Epileptic seizure. The glia cells are dynamic in nature, and they can be temporary out of order but are healthy and can rejuvenate themselves with own cell mitosis of course, some rare cases due to genetic genome or life style epigenetic phenome reasons, glia cell can be developing toward tumor (benign type & malign glioma type 1 to type 4 according to United Nations, World Health Organization, e.g. Senator John McCain has diagnosed glioma in July 2017 after local surgery, he is rapidly worsen to the terminating stage-4 by April 2018). Multiple sclerosis is another glia causing autoimmune disease that our own immune cells attack and destroy the Myelin sheath. The immune system might be fighting the infection by a virus mistaking Myelin sheath for a viral protein because it resembles the previouslyrecognized viral invader. We are describing a healthy brain to causing occasional fuzzy possibility thinking, and definitely not pathological reasons, as this might be proved by founder Lotfi Zadeh who lived healthy & productive until 98 years old without brain disorders.

Unification theory between normal brian and fuzzy brian
We wish to unify the human brain biological neural networks (BNN) with the brain isothermal natural intelligent (NI)) with Lotfi Zadeh fuzzy logic and Walter Freeman ion diffusion dynamics. We postulated a homeostasis equilibrium theory of human brains which have two states: input state from the dendrite tree to the output state at axon hillock where the potential drop is derived from the Maxwell-Boltzmann (2 nd &1 st from LHS of Figure 1) Canonical probability. It turned out to yield the normalized sigmoid function of neuron firing rate. This is first observed in 1943 by Warren S. McCulloch (3 rd ), a neuroscientist, and Walter Pitts (4 th ), a logician, in Figure 1. In this paper McCulloch and Pitts tried to understand how the brain could produce highly complex logic prior to John von Neumann (5 th from LHS) designing the computer logic. [1][2][3][4]  Ludwig Boltzmann introduced the concept of total entropy S as the measuring the degree of uniformity. For example, the mountain top rock has much less entropy than white sand beach Thus, human brain temperature is kept at 0 o T =37 C which is slightly higher than the thermal reservoir energy which is optimum for the elasticity of red blood cell hemoglobin. On the other hand, the chicken is kept at 40 °C for reason of hatching eggs. However, a higher temperature of brains is not necessarily to be smart, because we "ate chicken, not vice versa. Q.E.D." Maxwell-Boltzmann Probability W is derived from the third thermodynamic Neal's law at non-zero temperature that insures the incessant collision mixing homogenizing the degree of uniformity measured by the total entropy  Figure 2).
Theorem 1: Riccati nonlinear 1 st order differential equation is derived from Maxwell-Boltzman two state weighted sum and its exact solution turns out to be the sigmoid threshold function ( ) Proof:  (4). (Note that in dynamical systems theory, the baker's map is a chaotic map from the unit square into itself. It is named after a kneading operation that bakers apply to dough: the dough is cut in half, and the two halves are stacked on one another, and compressed. cf. Wikipedia)

Proof:
We introduce the calcium ions ( ) x ϕ concentration; we can set the slope of logarithmic concentration to be two-state normalization sigmoid With respect to a local wave front, the streaming term is set to zero at the wave front, e.g. sitting on the smoke outer most wave front Figure 3 where smoke particles will be diffusive.
Where Vt r = the quadratic parabolic curvature is reduced through the collisions among Calcium ion particles and cellar medium molecules into a linear trajectory ( Figure 4). However, when the active ushering glia cells are temporarily out of order, these ions cannot keep up with the ions passing rate, the output rate my dip in piecewise negative slope: the more inputs are, the less output are. The ions are stuck in the Axon Hillock ( Figure 5).
The quadratic sigmoid map follows M. Feigenbaum bifurcation logistic map with 4 λ knob turning higher value that might depend on the physiologic happy Hormone Dopamine or glia cells cooperation or not ( Figure 6).  Physiology experiments: Neurobiologists have observed the sudden onset of Epileptic seizure when the two states are crossed over becoming a pseudo-synchronous. The root cause could be the crossover output axon without insulating Myelin sheath due to Epileptic seizures the output short circuit the input dendrite tree in Figure  4B. Multiple sclerosis is another glia causing autoimmune disease that our own immune cells attack and destroy the Myelin sheath. In these cases, Takeshi Yamakawa has demonstrated by using real-time Magnetic imaging the physician can apply a laser pipe in to burn at the cross-over junction. The less invasive procedure has turned the Hospital week-long patients into a day visit out-patient (Figure 7) (Figure 8).

Figure 4
Indicate the complexity of ion current reservoir that (Wikipedia) might go wrong. A single layer of the membrane is built with hydrophilic heads and hydrophobic tails (like a human heads and legs) in three inter-related inserts in the RHS. The potential at the Axon Hillock (LHS sub-figure) has about ~100-200 voltage-gated sodium channels per square micrometer. Both inhibitory postsynaptic potentials and excitatory postsynaptic potentials are summed in the axon hillock and once a triggering threshold is exceeded, an action potential propagates through the rest of the axon (and "backwards" towards the dendrites as seen in neural back-propagation).

Figure 5
Chaotic Neural Net will be due to a piecewise negative N-shape logic in the sigmoid logic.

Isothermal brain predicting Mcculloch-Pitts logic implicating Walter freeman ionic diffusion and Lotfi
Zadeh fuzzy logic that might be useful for coding autonomous vehicles to be coexisting with the pedestrians

Applications to Autonomous Vehicle (AV)
Flow Imaging Processing is adopted for collision avoidance situation awareness. were in no-man land. Highway TSA said semi-DAV at level 4 will be dozen years, circa 2030. DAV machine must be peacefully co-exited with crowded human society with all kinds of personality. Automation computer scientists need to endow machines with 3 rd Gen AI to comprehend human fuzzy possibility thinking, so-called Zedah-Freeman fuzzy logic, in order to exit with human being society. Of course, fuzziness is not the logic, but open set Fuzzy Membership Function's (FMF's)) e.g.,"Young", or "Beautiful." A double fuzziness "Young & Beautiful" becomes less fuzzy. That's why we endow FMF's at execution load time to the digital machine. [5][6][7][8] Isothermal brain predicting Mcculloch-Pitts logic implicating Walter freeman ionic diffusion and Lotfi Zadeh fuzzy logic that might be useful for coding autonomous vehicles to be coexisting with the pedestrians E. To increase probability of detection of A & minimize False Alarm Rate B we need multiple layers in the so-called deep learning (Figure 9). We wish to improve the supervised deep learning with LMS cost to become self-organization "follow the leader" as Unsupervised Deep Learning with thermodynamic equilibrium at constant temperature o T at Minimum Free Energy (MFE). The automation solves NP Complete path finding problem by means of loss-less divide and conquer (ANN TSP, Foo & Szu, 1997). Supervised cost function is taken as , the cost of search for C  city is linear at boundary. We review thermodynamics to answer why keep our head blood temperature constant 37 0 C. This is necessary for the optimum elasticity of red blood cells Hemoglobium, squeezing through capillaries supplying the glucose and oxygen. Also, the thermodynamic equilibrium keeps the chemical diffusion rate constant for all generations to accumulate the experience. This is the basis of human Natural Intelligence (NI) based on two necessary conditions: Langevin equation of the car momentum P mV =   , with tire-road friction coefficient f ,car-body aerodynamic fluctuation force ( ) This possible membership concept is important to exploration of large data as which often don't have definitive membership relations when partial analysis of the data is being done without definite knowledge that classifies all the subsets of the data. For example, "young and beautiful" is a much sharper possibility than either "the Young" or "the Beautiful". When we average over spatial cases, we obtain the average of the experience based Expert System in order to elucidate i-AI.

Brake FMF Sensor Awareness FMF GPS space time FMF Experience stop
Review of fuzzy membership function, which is an open set and cannot be normalized as the probability but a possibility ( Figure 10). UC Berkeley Prof. Lotfi Zadeh passed away at the age of 95 years old and Walter Freeman at age 89. To them, 80 may be "young." Likewise, the "beauty" is in the eye of beholder. According to the Greek mythology of Helen of Troy, has sunk thousand ships, and Egypt Cleopatra hundred ships and Bible Eva one ship (Noah Arc) ( Figure 11). Consequently, the car will drive through slowly when the red light happens at the mid night in desert and without incoming cars. Such an RB becomes flexible as EBES. To show that this replacing RB with EBES is a natural improvement of AI in the remaining paper. This explains a driverless car that will turn the rule stopping at red light to be gliding over the red light when no incoming car at mid light in desert. [10][11][12][13][14][15][16]

Conclusion
We demonstrate an application of Lotfi Zadeh fuzzy membership function of two states "beauty or not" (Figure 12). In summary, Russian Mathematician G Cybenko 2 has proved "Approximation by Superposition of a Sigmoidal Functions," Math. Control Signals Sys. (1989)2:303-314. Similarly, Kolmogorov AN 3 has given "On the representation of continuous functions of many variables by superposition of continuous function of one variable and addition,"Dokl. Akad. Nauk, SSSR, 114(1957), 953-956. The two state normalization in the Maxwell-Boltzmann phase space distributions is derived to be equivalent to an ion-current diffusion equation, as proposed first ad-hoc-ly by Walter Freeman. By means of the Hopf transform, we can be applied to the sigmoid threshold logic, which turns out to be fuzzy membership function (FMF) of beauty or not. We have illustrated the two states normalization.