Research Article Volume 6 Issue 1

^{1}Bio-Med. Engineering, Catholic University of America, Wash DC, USA^{2}National Cheng Kung University, Taiwan^{3}Chung Yuan Christian University, Taiwan

**Correspondence:** Harold H Szu, PhD (The Rockefeller U), Fellows (AIAA, INNS, AIMBE, IEEE, OSA, SPIE) Academician (RAS) (RNL. S. V. Malrosov, 135, 1999), Res Ord Prof, CUA, Wash D.C, USA, Tel 12023195000

Received: November 15, 2022 | Published: November 30, 2022

**Citation: **Szu HH, Lum P, Tang MJ, et al. Digital & analog information loss for aging toward reversing. *MOJ App Bio Biomech*. 2022;6(1):35-43. DOI: 10.15406/mojabb.2022.06.00165

We match ** Health spans** with

During the maturity of cells, a general belief in aging is a slowly loss of digital genomic info as well as analog epi(outside)-genomic namely phoneme info (cf. Figure 1). Then, these bio-info-retrieval processing could be a graceful aging toward reverse aging. Nonetheless, ** according to the physics of irreversible thermodynamics**, the

**Figure 1** (a) Sir Charles Darwinian Phenotype (common descent, gradualism, multiplication of species, and natural selection) versus Fr. Gregor Mendel Genotype (computational); (b) 23 pairs of X & Y shaped chromosome made of double helix A-T& C-G pairs discovered by ** Jim Watson, Francis Crick, Rosaline Franklin** (did X-ray cryptography 51; died of oval cancer 1958 before the announcement of Nobel Prizes. When each untwined it will be about 3 meter long, that’s why the epigenetic information is necessary

For example, the ** Eukaryotes** cells have nuclei of DNA’s, of which the systems have both analog phenome and digital genome information. Thus, we must generalize the digital Shannon information to include the analog

*For example, FDA recommended taking**Elysium matter*** Long-Term Brain Health **manufactured in New York; Oxford University has developed a double blind protocol with the Gold Standard (double blind (NY and Oxford/Patients), negative control using placebo; sufficient statistics about 168 in 2 years) with proven mixture of Vitamin B complex and Omega-3 Lysine Complex extracted from coral reefs, sea grass beds, and mangrove forests

$\frac{1}{2}\xb7\frac{1}{2}=\frac{1}{4}$ (1)

(a) In order to provide *Homo sapiens*** fast sensory systems,** we can understand why we always have the power of pairs, 2 eyes, 2 ears, 2 nose holes, 2 sides of tongue, 2 hands, “

** Harry Nyquist Sampling Theorem 1959**: a simultaneous 2 samples per period:

*Prof:*** Multiply Planck constant** $LHS=\hslash 2\pi f=\hslash \omega =E=\hslash {c}_{o}k=\hslash {c}_{o}\frac{2\pi}{\lambda}=\hslash {c}_{o}\frac{\pi}{d}=RHS,$
where use is made of $\omega \equiv {c}_{o}k$
photon linear dispersion law. *Nyquist *concluded $\lambda =2d$
; where ** d** is the half optical (microscope) wave length: $\lambda /2$

(b) Secondly, we refer to Prof. ** David A. Sinclair** of Harvard Medical School who has written a best-seller book “

Moreover, the ** dynamic proofreading mechanisms** of

** NIH/NIA Former Director Mark P. Mattrson** has proposed how to

Recently, Stanford CS Dept Prof. ** Andrew Ng** has applied efficient

**Figure 2**

- Co-evolution partners
*Eukyote*are indicated as about 100 or so(*Mitochondria Organelle***O.)**which can efficiently rotate themselves to add a phosphate atom back to Adolescence Double Phosphate àchemical inside an Eukaryote cell of Homo sapiens. If we define young to be preserving both analog and digital information, while the otherwise as old.*ATP* - This including the possibilities of their young or old.
per mole*7.5 kilo calories***(iii)**Reversible*ATP<—>ADT***(iv)**Brains will use daily 20% of our whole body energy, as one feels hungry after study, but unfortunately the waste Brain Burning By-products) must be secreted outside of the*(BBB*by sleeping tight in those 6 Dimensions (3 physical + 3 mental) prevention for*brain blood barrier (bbb)*: (1)Regular Exercise, (2) Healthy Diet, (3) Quality Sleep,*Dementia Alzheimer Disorder (DAD: 3 Physical Dimensions*: (*3 Mental Dimensions***4**) Social Engagement, (**5**) Mental Stimulation, (**6**) Stress Management.

**Figure 3**

a) Harvard Med Sch. David A. Sinclair;

b) Harvard Syst. Biol. Marc W. Kirschner;

c) Princeton U. John J. Hopfield;

d) NIH/NIA Mark Mattrson (cf. 18 hours fasting facial collaping);

e) Stanford Andrew Ng;

f) Hippocampus/Amygala,

g) type of neuroglia(90% of the central nervous system is made up of neuroglia).

(c) Prof. ** Marc W. Kirschner** Founding Chair of System Biology Dept. of Harvard, advocated mathematics approach to Investigate biological organization in space and time, e.g. cytoskeleton, the regulation of the cell cycle, and the process of signaling in embryos, as well as the evolution of the vertebrate body plan, e.g. microtubules established their unusual molecular assembly from

In order to generalize aforementioned information theory, we will explore explicitly ** Human Visual System (HVS)** as an indication a potential

(i) Without light, HVS will have a flow of “** Dark Currents (Ca++)”: meaning no incoming photons yet,”** circulated

$sX=\mathrm{exp}(U);U=\mathrm{log}X+\mathrm{log}s;e.g.sizes=2,WeperceiveU\sim \mathrm{log}2\cong 0.3$ (2)

$\Delta {X}_{90}\Delta {P}_{1}\cong \hslash $ (3)

**Figure 4** The bundle of 90 rods are distributed in polar exponential coordinates is flowing with Dark Ca^{++}Currents, as discovered by NIH/DDKD William Archer Hagins.

**Figure 5** Model of Neural Net by Cornell Univ. *Frank **Rosenblatt single layer neural net exhibited at Smithsonian **Museum.*

**Figure 6** Directional Vector Information Flow Theory which can be recursively going down small bits segments. Eventually, we have algebraically reduced to orthogonal segments within the channel capacity, which can be furthermore digitized.

Bit pair:{(1111,0000) to (0000,1111)};

Bit pair: {(11,00) to (00,11)};

Bit pair: {(1,0) to (0,1)}.

**Figure 7** Former 9 Scientists have left us with their wisdoms a. Charles Darwin, b. Ludwig Boltzmann, c. Allan Turing, d Claude Shnnon, e. Marvin Minsky, f. Stanford John McCarthy, g..Hermann Helmholtz, h. William Archer Hagins, i. Alex Lyaponov (Is’nt that a shame all these 9 great scientists have gone from the Earth.)

Moonlight chase, a pray size has changed by a factor of 2 is only changed about 0.3 at Cortex 17, we are easier to aim at the prey; (a) This is called gracefully scale invariant; (b) Schrodinger Quantum Mechanics Uncertainty Principle, where the Planck constant $\hslash \equiv h/2\pi $ .

These **dark currents** were first discovered by ** William A. Hagins of NIH**. If there were

Evolutionally speaking we have thus far separated the “** energy from information**” so that “

(1) British: ** Alan Turing tested the other side to be Human or computer?**;

(2) MIT: ** Marvin **Minks disproved Cornell Univ.

(3) Stanford ** John McCarthy** gave

Information $I\equiv -{\mathrm{log}}_{2}p={\mathrm{log}}_{2\frac{1}{p}}$ (4)

For example, digital answer is “either yes, “1” or no, “0”, each with a half chance:

Given Eq. (4) $\because {p}_{yes}=\frac{1}{2};{p}_{no}=\frac{1}{2}\therefore {I}_{yes}=1;{I}_{no}=1.$ Q.E.D.

Since English has **26** letters (a,b,c,..,x.y.z, ) plus a blank **space**, then Shannon considered 27 different characters in the message, and the information content of each letter is estimated by ${I}_{no}=1.I=-lo{g}_{2}\left(\frac{1}{27}\right)=4.75bits$
. For series of n characters, Shannon gave the average information called the ** entropy** ${H}_{Shannon}$
.

${H}_{Shannon}\equiv {\langle I\rangle}_{ave}\equiv -{\sum}_{i=1}^{n}p{\mathrm{log}}_{2}{p}_{i}$ (5)

The Shannon restoration involves a *divide-and-conque*r concept for amplification and truncation at each individual bits level. We wish to adopt a vector time segments generalization of Shannon theory. At the other side of the channel,before these bits have been combined into the full digital information. We shall now review ** Ludwig Boltzmann** definition of entropy in order to generalize

Thus we estimate for warm body temperature ${37}^{o}C\equiv 31{0}^{o}K;$ we estimate 1/37 eV, because $9\cong \frac{27}{37}=\frac{\frac{1}{40}}{\frac{1}{37}}=\frac{37}{40}\cong 9$ equilibrium at the minimum Helmholtz free energy ${H}_{in}$ as follows:

We begin with Ludwig Boltzmann definition of entropy as the measure of the degree of uniformity which includes the internal and external systems. In other words, the entropy is a measure of unusable energy when multiplied by the temperature ${T}_{0}=31{0}^{0}K.$
. For example, the rocks on mountain top have more degree of non-uniformity than erosion down to river beach sands, and thus more useful archeological information than uniform sand. Ludwig Boltzmann wrote down on his headstone (without the subscript **B**) and we shall adopt $Log\equiv Ln\equiv {\mathrm{log}}_{e};e=2.71\mathrm{8...},$
,

$S={k}_{B}LogW;$ (6)

Probability measure is given as the inverse:

$W=\mathrm{exp}\left(\frac{S}{{k}_{B}}\right)=\mathrm{exp}\left(\frac{({S}_{out}+{S}_{in}){T}_{o}}{{k}_{B}{T}_{o}}\right)=\mathrm{exp}\left(-\frac{{H}_{in}}{{k}_{B}{T}_{o}}\right)$ (7)

Where use is made of theHomeostasis conservation law to introduce Helmholtz free energy:

$\because {S}_{out}{T}_{o}+{E}_{in}=0;\therefore {S}_{out}{T}_{o}=-{E}_{in};$ (8)

Replacing the outside unknown entropy with ** internal expenditure of energy**, we have derived Herman Helmholtz “free to do work” energy at the constant body temperature ${T}_{o}$

${37}^{0}C=31{0}^{0}K\cong \frac{1}{37}eV$

${H}_{in}\equiv {E}_{in}-{S}_{in}{T}_{o}$ (9)

** Theorem Unsupervised Deep Learning for feature extraction:** Newtonian Equation of Motion of neuronal interconnect weight matrix $\left[W\right]$

$\stackrel{\rightharpoonup}{y}(t)=\left[W\right]\stackrel{\rightharpoonup}{x}(t);\stackrel{\rightharpoonup}{z}(t\text{'})=\sigma [\stackrel{\rightharpoonup}{y}(t)]$

Deep learning is based on multiple layers, $\stackrel{\rightharpoonup}{x},\stackrel{\rightharpoonup}{y},\stackrel{\rightharpoonup}{z}$

$\frac{\Delta [W]}{\Delta t}=-\frac{\Delta {H}_{in}}{\Delta [W]}$ (10)

We have proved the unsupervised learning in ** Lyaponov **monotonic

$\frac{d{H}_{in}}{dt}=\frac{\partial {H}_{in}}{\partial [W]}\frac{\Delta [W]}{\Delta t}=-{\left(\frac{\partial {H}_{in}}{\partial [W]}\right)}^{2}\le 0$ (11)

The threshold logic will be different for different applications $(\beta \equiv \frac{1}{{k}_{B}{T}_{0}})$

$\frac{\mathrm{exp}(-\beta {H}_{in})}{\mathrm{exp}(-\beta {H}_{in})+\mathrm{exp}(\beta {H}_{out})}=\frac{1}{1+\mathrm{exp}(-\beta ({H}_{out}+{H}_{in}))}\equiv \sigma (x)$ (12)

Of course this is not the only threshold logic, there is other rapid computation threshold logic, as well as ** N-shaped ** ${\sigma}_{N}(x)$
that can generate a

$DOn=1,2,e.t.c{\left|{\stackrel{\rightharpoonup}{b}}_{n}\right|}^{2}={\left|{\stackrel{\rightharpoonup}{b}}_{n+1}+{\stackrel{\rightharpoonup}{b}}_{n+2}\right|}^{2}={\left|{\stackrel{\rightharpoonup}{b}}_{n+1}\right|}^{2}+{\left|{\stackrel{\rightharpoonup}{b}}_{n+2}\right|}^{2},iff{\stackrel{\rightharpoonup}{b}}_{n+1}\perp {\stackrel{\rightharpoonup}{b}}_{n+2}$ (13)

Nonetheless, each segment information can be digitized into pair signal vector will suffer the propagation spreading (envelope of wave front, known as Huygens wavelets law) as well as channel noisesexerted upon every wave-fronts. As a result, the noise will be likewise amplified near the receive station with a weaken spread signal.

$TruncateafterAmplification\u301a\stackrel{\rightharpoonup}{b}{}_{l}(t)+\tilde{n}\u301b\cong \stackrel{\rightharpoonup}{b}{}_{l}(t+\tau );\tau 0$ (14)

Biologically speaking, Eq. (14) is replaced by error correction back tracking. That’s the same reason why the original information is orthogonally divided into bit stream, when degraded by channel propagation will be amplified and restored back bits by bits to a maximum possible upper limits of bits stream. Within a large error margin, we can exactly reproduce the original digital information. This is Shannon Information Theory. For example, an English message is represented into binary bits stream and then each bit may suffer with unavoidable channel spreading and noise but will be amplified and truncated into bits overcoming the noisy amplification before been re-combined into original English.

(iv) Can AI help Graceful Aging toward even the mythical Reverse Aging? This question implies that AI must enhance those 4 chances, namely 2 co-evolution species (Homo Sapiens & Mitochondria) x 2 states (Young & Old). This capability is the most important for ** WWII Baby Boomers** in order to utilize their

** ATP** become

**The Food and Drug Administration ( FDA) has banned NMN for sale as a supplement, citing its status as under investigation as a drug*.

*How do we know two species are not just one species?*

*Proof***:** Homo sapiens species receive half genes from mother side and the other half from father side. This mixed fact allows the choice of healthy ones. On the contrary, Mitochondria are passing down only from the maternal side, not from the paternal side (less chance for Darwin-like evolution theory “the fittest, the survival”).

Note that male sperm does have mitochondria line up along its tail to power its wagging tail to seek & break into the egg, but once the sperm head enters a mother egg, immediately the egg cell will be closed up, to prevent a second sperm or even the first tails to enter. Only the mother egg can house100 or so mitochondria and will pass on to the next generation.** **

Once we accept the fact of two species, then the reverse aging truth table will have 2x2=4 entries. We at least have to take 4 actions as follows: Given

(1) Metformin (made originally from French Lilac flowers, 1 gm per day in two pills according to the US FDA approved Protocol TAME (Target Aging Metformin) campaigned by Dr. Nir Barzilai, Albert Einstein Medical School to reduce blood sugar and henceforth our body fat reducing body weight;

(2) NMN can enhance NAD+ to mediate communication between our cells and Mitochondria organelle partners. Furthermore, we need

(3) to get rid of old cells by "intermittent fasting" for about 12 hours without food intakes, so that old senescence cells can be apoptosis: self-programming death;

(4) Exercise daily to “use them or loss them.” so that the inefficient Mitochondria will replenish themselves (we don’t know exactly how?)

Chinese Colloquium said well: Take ones breakfast like a king or queen, lunch as Prime Minister, dinner like a beggar. German Colloquium said that “The longer the belt is, the shorter, the life will be. “German said” The longer, the belt is; the shorter the life will be”.

When this is" in", there must be "out". Nonetheless, the degree of uniformity in terms of so-called Entropy will increase, while the information will be reduced. We Homo sapiens have co-evolution partners about 3~4 billion years ago. Our cells swallow about 100 or so Mitochondria organelle. (MO: known as double membrane bacteria, but never come out). They stayed on to produce chemical energy from ATP to ADP losing a phosphate by water hydrolysis giving rise to 7 Cal molar heats. On the one hand, Mitochondria malfunction will produce several neurological disorders. On the other hand, cells keep differentiations and give birth to more cells until nowadays Homo sapiens mankind. Thus, whether we are young or old must be based on these 2 body problems with 1/4 probability for success or failure. (1) Exercise daily by R.S.T.U.V. Ben Lo principles of CMC-37 Tai Chi Q’uan to replenish weak Mitochondria organelle; (2) Eat right by intermittent fasting about 12 hours to make senescent cells apoptosis; (3) Sleep tight to clean up 20% brain energy cloggy by-products to avoid Dementia Alzheimer Disorder; (4) Social Often wearing a smile meeting the others who may be in the same boat as you are, (5) Stimulate brains to use them or loss them, (6) Relax mind "Deep Breathing, Don't Worry!" Do your best and God will do the rest" said by Mr. Wang C-S (**王建****瑄**) who have influenced other leader to help built K-12 education in remote area of China.

Once we accept the fact of two co-evolutional species, then the reverse aging truth table will have **4 **entries. We at least have to take 4 actions as follows: Given** $\frac{1}{2}\xb7\frac{1}{2}=\frac{1}{4}$
. **Useful guidance from graceful aging to revere aging are given, **People have sought after medicines or food supplement to enhance the probability as follows:**** **

(1) ** Metformin** (made originally from

(2) *NMN**N***icotinamide ***M***ono***N***ucleotide, **made off with side chains around a pentagon & a hexagon similar to hormones (debatable as a food supplement without side effect or not within FDA), and how the powder shall be admitted under the toque capillaries in order to be by-passing acid stomach digestion. The fact of matter it is still a precursor that can enhance ** NAD+** (Nicotinamide adenine dinucleotide) mediating the communication between our cells and co-evolution partners MO. Furthermore, we need

(3) "** Intermittent Fasting**" about 12 ~18 hours, so that old

(4) **Exercise daily** to “.” so that the inefficient *Mitochondria*** Organelle** will be used or loss it by replenish themselves.

(5) We need to **sleep tight** (with the help of warm sucks, ear plugs, knee pillow) longer ** than 8 hours** to clean up energy byproducts from our brains

(6) Lastly, we need to relax mind: Don’t Worry: While in the East, we have motto: “Do your best and God will do the rest”; in the West, we have Sound of Music “Que So la, So la, whatever will be, will be. The future is not ours to see.” (Quote from Sound of Music Sister Maria & Captain von Trout).

Besides the wealthy Executive Chairman of *Amazon* ** Jeff Bezos**, who has invested $3B on

As a matter of fact, if the mother’s inheriting mitochondria were sick, physician will adopt foster mother egg’s mitochondria, as if 3 parents offspring’s, but replace its egg nucleus with the mother nucleus, cf. (Figure 9).

**Figure 11** ThreeYour thymus gland (not Thyroid at throat) is located just in front of and above your heart.

https://www.forbes.com/sites/calcumchace/2022/11/01/regerating-the-thymus-pofile-of-greg-fahy/?sh=3f48d445d2eb

Since there are two partners that require both to replenish themselves by (a) reducing the wasteful old cell by ** intermittent fasting** (12 ~18 hours) and (b) Mitochondria to replenish themselves by we

Your thymus gland (not Thyroid at throat) is about an ounce, and located just in front of and above your heart. Thymus gland can secrets immune T-cells to kill bacteria, virus, etc. Recently, scientists found that T-cells can eliminate our aging senescent cells.

**Background:** Almost 4 billion years ago, when the ** Eukaryotes** cells swallowed 100 or so

*Marc W. Kirschner***, Harvard Sys. Biology **emphasized cellular dynamics including the treadmill dynamics **in “ Cells, Embryos, and Evolution;” and “Plausibility of Life: Resolving Darwin¹s Dilemma**”. Meanwhile,

In conclusion, we must explore all possible info retrieval mechanism; we need to execute ** John McCarthy** Stanford Artificial Intelligence as well as the modern day

*Appendix A*

(1) to make nursing home ** humanoids robots **processing all sensory data inputs, including voice tone & body language, in order to perceive the emotion of

**Figure A1** Min. Negative Rate that may inadvertently delay the patients to see physicians.

National Library Medicine (National Library of Medicine - National Institutes of Health (nih.gov)) make in ARS (age, race, sex), in NIH Bethesda Campus of 27 Institutes shared a Network of informed decisions about their health to reduce ** False Neg. Rate** that may inadvertently delay the patient treatment time;

**Figure A2** General Chairman Steve Grossberg of the first IEEE International Conference on Neural.

Networks (ICNN) in 1987 and played a key role in organizing the first INNS annual meeting in 1988, H. Szu has served as the Founding Secretary and Treasurer of INNS offered by Steve Grossberg during SPIE Optical and hybrid computing : 24-27 March 1986, cf. Appendix A, Dr. Harold H. Szu, Editor; Dr. Roy F. Potter, (v. 634., SPIE, National Library of New Zealand) at Xerox International Center for Training and Management Development, Leesburg, Virginia where Dr. Robert ** Hecht-Nielsen** (ASU in math) with the financial support of DARPA Dr. Helena

**Appendix B attendances**

PROCEEDINGS VOLUME 634 Dr. Harold H. Szu, Editor; Dr. Roy F. Potter, | 24-27 MARCH 1986 **at Xerox International Center for Training and Management Development, Leesburg, Virginia**

- James Ionson
- J. P. Boris
- John A. Neff
- Satoshi Ishihara
- VanderLugt
- William T. Rhodes
- William Stoner

Francis T. S. Yu

- J. Caulfield; Mustafa A. G. Abushagur
- Ravindra A. Athale
- Desmond Smith; Andrew C. Walker; Brian S. Wherrett; Frank A. P. Tooley
- M. Gibbs; N. Peyghambarian
- W. Lohmann; J. Weigelt
- Toyohiko Yatagai
- Steven C. Gustafson; Steven L. Cartwright; David L. Flannery; Gordon R. Little; John S. Loomis; L. Maugh Vail
- Forrest L. Carter
- Simic-Glavaski
- Teuvo Kohonen
- James A. Anderson; Richard M. Golden; Gregory L. Murphy
- Nabil H. Farhat
- Sam Horvitz
- Bill Miceli
- Arthur D. Fisher; John N. Lee
- William S. C. Chang; H. H. Wieder; T. E. Van Eck; A. L. Kellner; P. Chu
- Fainman; Sing H. Lee
- P. Kenan; C. M. Verber
- Chen S. Tsai
- D. Henshaw; A. B. Todtenkopf
- David Casasent
- Thomas F. Krile; John F. Walkup

**Appendix B Key Papers abstracts**

**Three Layers Of Vector Outer Product Neural Networks For Optical Pattern Recognition**

Author(s): Harold Szu

A single homogeneous layer of neural network is reviewed. For optical computing, a vector outer product model of neural network is fully explored and is characterized to be quasi-linear (QL). The relationships among the hetero-associative memory [AM], the ill-posed inverse association (solved by annealing algorithm Boltzmann machine (BM)), and the symmetric interconnect [T] of Hopfield's model E(N) are found by applying Wiener's criterion to the output feature f and setting [EQUATION].

**Nonlinear Signal Processing Using Fiber-Optics Neurograms**

Author(s): Harold Szu

A novel optical device for nonlinear signal processing is described based upon the following observations: (a) A phase space for signal processing is identified with a time-frequency joint representation (TFJR) that appears almost everywhere naturally, for example in bats, in music, etc. (b) A sudden slow down mechanism is responsible for the transition from a phase coherent-to-incoherent wave front and provides us the sharpest tone transduction from a Bekesy traveling wave in a model of the inner ear.

**Computed Tomography For Optical Computing**

Author(s): Harold Szu

All known methods of computed tomography (CT) for image reconstruction from parallel projections have been derived from Fourier transform (the central slice theorem) and inverse Fourier transform, and the present Hankel transform tomography being an angular slice theorem is of no exception. Such a simplified viewpoint and unified theory is expected to serve the reader of optical computing and to pool interdisciplinary knowledge from a broader scientific community. The community can apply CT to optical computing or innovate novel approaches to solve the problem of real time and safe dosage computed tomography.

**Holographic Coordinate Transformations And Optical Computing**

Author(s): Harold Szu

The alignment problem among an object o (7), the OFT lens and a phase hologram exp(iφ(r)) is investigated for holographic coordinate transformations, both theoretically and numerically, using FFT replacing OFT for two interesting examples in human visual systems. The optimum alignment is found to be at a specific saddle point r = r0 of the phase hologram defined by Δφ(r0)= k = 0 and Δ2φ = 0 where the OFT lens axis k = 0 (D.C.) and the object origin r = 0 must be overlayed. The result of such a D.C.-saddle point alignment can be understood in terms of the minimization of high order (cubic and above) contributions of the Fourier phase integral from a general viewpoint of a stationary phase approximation. the slowdown is physically identified to be due to three forces. This has been used to derive a cubic deceleration polynomial responsible for a cusp bifurcation phenomenon which occur for every tone transducted along the nonuniform elastic membrane. The liquid-filled inner ear cochlea channel is divided by the membrane into an upper duct that has hair cells for the forward sound-generated flow and the lower duct for the backward balance-return flow.

**Iterative Restoration Algorithms For Nonlinear Constraint Computing**

Author(s): Harold Szu

We sometimes wish to undo what has been done to optical data using repeatedly identical nonlinear optical processors, such as non-linear imaging devices, matrix-vector multipliers with threshold logic, etc. This undoing is mathematically, equivalent to finding the inverse operator D-1, if the direct operator D represents the nonlinear optical processor in repeated usage.

**Nonlinear Signal Processing Using Fiber-Optics Neurograms**

Author(s): Harold Szu

A novel optical device for nonlinear signal processing is described based upon the following observations: (a) A phase space for signal processing is identified with a time-frequency joint representation (TFJR) that appears almost everywhere naturally, for example in bats, in music, etc. (b) A sudden slow down mechanism is responsible for the transition from a phase coherent-to-incoherent wavefront and provides us the sharpest tone transduction from a Bekesy traveling wave in a model of the inner ear. The cause of the slowdown is physically identified to be due to three forces. This has been used to derive a cubic deceleration polynomial responsible for a cusp bifurcation phenomenon which occurs for every tone transducted along the nonuniform elastic membrane. The liquid-filled inner ear cochlea channel is divided by the membrane into an upper duct that has hair cells for the forward sound-generated flow and the lower duct for the backward balance-return flow.We sometimes wish to undo what has been done to optical data using repeatedly identical nonlinear optical processors, such as non-linear imaging devices, matrix-vector multipliers with threshold logic, etc. This undoing is mathematically, equivalent to finding the inverse operator D-1, if the direct operator D represents the nonlinear optical processor in repeated usage.

**Panel Discussion**

Author(s): Harold H. Szu

In introduction, we have Sam Horvitz who is in charge of this panel and who will produce the report. Our purpose is to review the state of the art in neural network computing as well as the connection with optical computing in the future. I'm sure there is a lot of controversy and interesting projections of the future that will come out of this meeting. Here is Mr. Horvitz.

**Computed Tomography For Optical Computing**

Author(s): Harold Szu

All known methods of computed tomography (CT) for image reconstruction from parallel projections have been derived from Fourier transform (the central slice theorem) and inverse Fourier transform, and the present Hankel transform tomography being an angular slice theorem is of no exception. Such a simplified viewpoint and unified theory is expected to serve the reader of optical computing and to pool interdisciplinary knowledge from a broader scientific community. The community can apply CT to optical computing or innovate novel approaches to solve the problem of real time and safe dosage computed tomography.

**Holographic Coordinate Transformations And Optical Computing**

Author(s): Harold Szu

The alignment problem among an object o (7), the OFT lens and a phase hologram exp(iφ(r)) is investigated for holographic coordinate transformations, both theoretically and numerically, using FFT replacing OFT for two interesting examples in human visual systems. The optimum alignment is found to be at a specific saddle point r = r0 of the phase hologram defined by Δφ(r0)= k = 0 and Δ2φ = 0 where the OFT lens axis k = 0 (D.C.) and the object origin r = 0 must be overlayed. The result of such a D.C.-saddle point alignment can be understood in terms of the minimization of high order (cubic and above) contributions of the Fourier phase integral from a general viewpoint of a stationary phase approximation.

**Associative Learning, Adaptive Pattern Recognition, And Cooperative-Competitive Decision Making By Neural Networks**

Author(s): Gail A. Carpenter; Stephen Grossberg

This article describes models of associative pattern learning, adaptive pattern recognition, and parallel decision-making by neural networks. It is shown that a small set of real-time non-linear neural equations within a larger set of specialized neural circuits can be used to study a wide variety of such problems. Models of energy minimization, cooperative-competitive decision making, competitive learning, adaptive resonance, interactive activation, and back propagation are discussed and compared.

**Performance Limits Of Optical, Electro-Optical, And Electronic Neurocomputers**

Author(s): Robert Hecht-Nielsen

The performance limits of optical, electro-optical, and electronic artificial neural systems (ANS) processors (also known as neurocomputers) are discussed. After a brief introduction, an overview is provided of the recently revived field of ANS. Next, ANS performance measures are defined and neurocomputer taxonomy is presented. Finally, the designs and performance limits of the various types of neurocomputers are discussed.

The first author H.S. wishes to acknowledge Fred & Ginny Wang, Willie & Clare Yang, Pastor Chu of Taipei Oneness Christ Church for their gracious hospitality & support.

None.

The author declares no conflicts of interest.

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