https://www.linkedin.com/in/jetem/

Scenario Optimization, Quantum Optimization, Complex Adaptive Leadership, Deal, NJ (2026)

10/22/2026

Innate immunity in disease.

Innate immunity serves as the body’s first line of defense, providing immediate protection while shaping subsequent adaptive immune responses.
Its effectiveness determines early disease outcomes and influences long-term immune memory and tolerance.
Understanding innate immune mechanisms enables the development of strategies to strengthen natural defenses and improve disease resistance.
Enhancing innate immunity represents a powerful approach for preventing and treating infections, autoimmune conditions, and chronic inflammatory diseases.

Active Feedback

A feedback path sends part of an amplifier’s output back to its input so the circuit stays stable and the gain is set by that path. Passive feedback uses a fixed resistor. Active feedback uses a biased transistor instead. The transistor’s resistance at the chosen bias becomes the feedback element, so the designer can change gain by changing bias rather than by changing the chip layout. The extra device adds a pole and a little noise. It is chosen when a resistor large enough for low noise would be too big or too slow to put on the chip.

Transimpedance Amplifier

A transimpedance amplifier converts a current into a voltage. In an optical receiver the current comes from a photodiode that turns light into charge. The amplifier’s input must look like a small resistance, so the diode’s capacitance does not set a slow time constant. The output must be a voltage large enough for the next circuit. The feedback element largely sets that volts-per-ampere gain. A larger feedback resistance gives more gain and less noise, and it also narrows the bandwidth.

Inductive Peaking

Every node on a chip has capacitance. With resistance, that capacitance rolls the signal off at high frequency. Inductive peaking adds a small inductor at that node. The inductor and the capacitance resonate near the top of the band and lift the response where it would otherwise fall. A modest lift extends bandwidth. A large lift rings and distorts pulses. The inductor must still behave as an inductor at the highest frequency in use, and it occupies area on the chip.

22 nm FDSOI CMOS

CMOS is the standard silicon process of complementary n-type and p-type transistors. FDSOI means the transistor sits in a very thin silicon film on an insulating oxide, so it is fully depleted of mobile charge at rest. The 22 nm figure is the process generation. Parasitic capacitance into the substrate is low, a back gate can tune the threshold, and the supply is typically under one volt. That suits a fast, low-power front end. Voltage headroom is small, so tall stacks of transistors are avoided, and the speed is spent on bandwidth rather than on large voltage gain.

How the four fit

The receiver needs a transimpedance amplifier. In this process the gain stage is simple and low power. Active feedback sets the current-to-voltage gain without a large resistor. Inductive peaking restores bandwidth taken by the photodiode capacitance. The circuit is judged by four measured numbers at the real diode capacitance and supply: transimpedance, bandwidth, input-referred noise, and pulse fidelity.
Grateful Direction Collaboration Coordination Convergence 44410 Convergence, Enlightened Goal, Determined Action, Best Outcome Situational Awareness, Accurate Information, Prudent Feedback

10/22/2026

3.41831597061124385292763138...

Compiler Pass Pipeline
A compiler pass pipeline is an ordered sequence of transformation and optimization passes applied to intermediate representations during compilation. Each pass analyzes or rewrites the code to improve performance, reduce size, or lower abstractions toward the target machine. In systems like MLIR, pipelines are nested and can target specific operation levels, enabling modular and reusable compilation flows. Proper pipeline design is critical because the order and selection of passes directly determine correctness and efficiency of the final code.

Generative AI
Generative AI refers to machine learning models, especially large language models, that create new content such as text, code, or structured outputs based on patterns learned from data. In compiler contexts, it can automatically produce or refine pass sequences by reasoning over domain knowledge and examples. These models reduce the need for exhaustive manual expertise by exploring valid combinations through techniques like knowledge bases and search. When applied to compilation, generative AI accelerates development while aiming for high success rates on complex tasks.

MLIR
MLIR (Multi-Level Intermediate Representation) is an extensible compiler infrastructure from the LLVM project that supports multiple levels of abstraction within a single framework. It allows dialects to represent computations ranging from high-level tensors and graphs down to low-level hardware instructions. Passes in MLIR operate on these dialects to perform progressive lowering, optimization, and conversion. This design makes MLIR especially powerful for domain-specific compilers, including those used in machine learning and hardware generation.

Ruler and Compass Constructions
Ruler and compass constructions are classical geometric procedures that create points, lines, and circles using only an unmarked straightedge and a collapsing compass. They generate exactly the lengths and points lying in successive quadratic extensions of the base field, corresponding to nested square roots. In the lemniscate setting these tools enable arc operations that mirror the addition formulas of elliptic functions. The resulting constructions remain purely geometric yet encode deep arithmetic structure from complex multiplication.

The Lemniscate
The lemniscate of Bernoulli is the figure-eight curve defined by \((x^2 + y^2)^2 = 2a^2(x^2 - y^2)\), whose arc-length integral involves the elliptic integral \(\int dt/\sqrt{1-t^4}\). Its inverse, the lemniscatic sine \(\varphi\), satisfies an addition law analogous to the trigonometric addition formulas, allowing arcs to be halved, doubled, added, or transferred with ruler and compass. Abel proved in 1827 that equal division of the lemniscate into \(n\) parts is possible precisely when \(n = 2^k\) times distinct Fermat primes. These geometric recipes therefore realize the arithmetic of the ring \(\mathbb{Z}[i]\) on the curve itself.

The 17-gon
A regular 17-gon is constructible with ruler and compass because 17 is a Fermat prime, so the real subfield of the 17th cyclotomic extension has degree a power of 2. The same arithmetic permits a regular 17-gon to be inscribed in the lemniscate: the division points are given by \(\varphi(2\omega k/17)\), where \(\omega\) is the complete lemniscate constant. Explicit radical expressions for the first vertex are obtained by solving a degree-4 equation over \(\mathbb{Q}(i)\) via successive square roots, after which the remaining vertices are generated by the arc-addition operations. The resulting lemnatomic 17-gon thus supplies a concrete geometric realization of both Gauss’s and Abel’s classical theorems.

Ruler and Compass Constructions
Ruler and compass constructions generate points and lengths by drawing straight lines and circles from previously constructed points, corresponding algebraically to quadratic field extensions. On the lemniscate these operations translate the addition and duplication formulas of the lemniscatic elliptic function into pure geometry. Consequently every constructible division of the curve can be realized by a finite sequence of such elementary steps. The same toolkit that builds the classical regular polygons on the circle therefore builds their analogues on the lemniscate.

Equilateral Triangle in the Lemniscate
The lemnatomic equilateral triangle consists of three points that divide one loop of the lemniscate into three arcs of equal length. Because 3 is a Fermat prime, Abel’s theorem guarantees that these points are obtainable by ruler and compass. Explicit constructions begin with the origin and the unit point, then apply a short sequence of arc-halving and arc-addition operations derived from Fagnano’s formula. The resulting three vertices form a regular triangle with respect to lemniscate arc length rather than Euclidean chord length.

Pentagon in the Lemniscate
The lemnatomic regular pentagon comprises five points that partition a lemniscate loop into five equal arcs. Since 5 is likewise a Fermat prime, the required division is constructible; the necessary radical expressions arise from a quadratic tower over \(\mathbb{Q}(i)\). Starting from a single fundamental arc obtained by solving a low-degree equation, repeated doubling and addition of arcs produce the remaining vertices. The finished figure is therefore a geometrically realized regular 5-gon measured by the elliptic arc-length of the lemniscate.

Energy Efficiency

Energy efficiency measures how effectively a system converts consumed energy into useful output, typically expressed as the ratio of delivered service to total power expended.

In wireless networks it quantifies the number of bits reliably transmitted per joule, reflecting both transmission and processing costs.

Improving energy efficiency extends battery life of user devices, reduces operational expenditure for operators, and lowers the environmental footprint of large-scale deployments.

It has become a central design criterion for 5G and 6G systems, especially in dense and non-terrestrial scenarios where power resources are constrained.

LEO Satellites

Low-Earth-Orbit (LEO) satellites operate at altitudes typically between 500 km and 2000 km, providing relatively low latency and high-capacity coverage compared with higher orbits.

Their rapid orbital motion requires sophisticated hand-over management and large constellations to ensure continuous service.

LEO platforms are a key component of emerging non-terrestrial networks, enabling global broadband access and backhaul for remote or mobile users.

When integrated with terrestrial systems they significantly expand coverage and support the ubiquitous connectivity goals of 6G.

Non-Terrestrial Networks (NTNs)

Non-terrestrial networks encompass communication systems that rely on airborne or space-borne platforms such as satellites, high-altitude platforms, and unmanned aerial vehicles.

They complement terrestrial infrastructure by providing coverage in remote, maritime, and disaster-affected regions where ground networks are unavailable or insufficient.

NTNs introduce unique challenges including long propagation delays, Doppler effects, and dynamic network topologies that must be addressed through specialized protocols and resource management.

In the 6G vision they form an essential layer of a fully integrated three-dimensional network architecture.

Semantic Communication

Semantic communication focuses on transmitting the meaning or task-relevant information of a message rather than its exact bit sequence.

By leveraging shared knowledge and machine-learning models at transmitter and receiver, it can drastically reduce the volume of data that needs to be sent.

This approach improves spectral and energy efficiency, particularly under severe bandwidth or power constraints.

It is regarded as a promising paradigm for 6G, enabling more intelligent and goal-oriented information exchange between humans and machines.

6G

6G refers to the next generation of mobile communication systems expected to succeed 5G, targeting extreme data rates, ultra-low latency, massive connectivity, and native artificial-intelligence support.

It aims to integrate terrestrial, non-terrestrial, and underwater networks into a seamless three-dimensional coverage fabric.

Key technological pillars include terahertz communications, advanced MIMO, semantic and goal-oriented communication, and pervasive edge intelligence.

The overarching goal is to enable immersive applications, holographic telepresence, and sustainable, globally accessible digital services.
Grateful Direction Situational Awareness, Accurate Information, Prudent Feedback Collaboration Coordination Convergence 44410 Convergence, Enlightened Goal, Determined Action, Best Outcome

10/19/2026

1, 5, 60, 1105, 27120, 828250, 30220800, 1282031525, 61999046400, 3366961243750, 202903221120000, 13437880555850250, 970217083619328000, 75849500508999712500, 6383483988812390400000, 575440151532675686278125, 55318762960656722780160000, 5649301494178851172304968750
Grateful Direction Situational Awareness, Accurate Information, Prudent Feedback Collaboration Coordination Convergence 44410 Convergence, Enlightened Goal, Determined Action, Best Outcome

10/18/2026

0, 7, 77, 777, 7777, 77777, 777777, 7777777, 77777777, 777777777, 7777777777, 77777777777, 777777777777, 7777777777777, 77777777777777, 777777777777777, 7777777777777777, 77777777777777777, 777777777777777777, 7777777777777777777, 77777777777777777777, 777777777777777777777
Grateful Direction Convergence, Enlightened Goal, Determined Action, Best Outcome Actual Win, Determined Success, Robust Strategy, Enlightened Effort

10/11/2026

CMOS, S-Parameters, Linearity, Noise Figure, Gain, and SNIM

CMOS is the process in which most radio front ends are built: complementary MOS transistors on a silicon substrate, with on-chip inductors, capacitors, and matching networks. Device \(f_T\) and noise improve with scaling, while supply voltage and intrinsic gain fall. Every later figure is a measurement of a CMOS two-port that must drive a \(50\,\Omega\) system and survive large signals.

S-parameters describe that two-port at RF. \(S_{11}\) is input reflection, \(S_{22}\) is output reflection, \(S_{21}\) is forward transmission, and \(S_{12}\) is reverse isolation. Power gain seen by the system is not raw \(S_{21}\); it depends on the source and load terminations. A design that quotes \(S_{21}\) without \(S_{11}\) and stability has not stated whether the power is delivered or reflected.

Noise figure is the degradation of signal-to-noise ratio through the block, \(NF = SNR_{in}/SNR_{out}\), usually in decibels. For a MOSFET the minimum noise figure \(NF_{min}\) occurs at a source admittance \(Y_{opt}\) that is not, in general, the admittance that maximizes gain. The four noise parameters \(NF_{min}\), \(R_n\), and \(\Gamma_{opt}\) fix how fast the noise figure rises as the source moves off that optimum.

Gain is the delivered power increase, reported as available gain, operating power gain, or transducer gain depending on which ports are matched. In a CMOS LNA the first stage sets the cascade noise figure by Friis’s relation: later stages matter only after the first-stage gain has suppressed their noise. High gain and low noise therefore compete for the same input match.

Linearity is the large-signal limit those small-signal numbers ignore. The \(1\,\mathrm{dB}\) compression point and the third-order intercept \(IIP3\) state when gain compresses and when intermodulation products rise into the band. A CMOS device biased for minimum noise is often not biased for best \(IIP3\). Feedback and degeneration that linearize the stage also move \(S_{11}\) and \(Y_{opt}\).

SNIM is simultaneous noise and impedance matching: the condition \(Z_{in} = Z_0 = Z_{opt}^{*}\) so the source that the system presents is also the source that achieves \(NF_{min}\), while reflections stay low. In a common-source CMOS stage this is not automatic. Inductive degeneration, reactive feedback, or an embedding network is used to pull \(Z_{in}\) and \(Z_{opt}\) together across the band. A successful SNIM design is one set of S-parameters, one noise figure near \(NF_{min}\), one stated gain, and one \(IIP3\) that still meets the blocker specification at that bias.
Grateful Direction Situational Awareness, Accurate Information, Prudent Feedback Collaboration Coordination Convergence 44410 Convergence, Enlightened Goal, Determined Action, Best Outcome

10/10/2026

Active Feedback

A feedback path sends part of an amplifier’s output back to its input so the circuit stays stable and the gain is set by that path. Passive feedback uses a fixed resistor. Active feedback uses a biased transistor instead. The transistor’s resistance at the chosen bias becomes the feedback element, so the designer can change gain by changing bias rather than by changing the chip layout. The extra device adds a pole and a little noise. It is chosen when a resistor large enough for low noise would be too big or too slow to put on the chip.

Transimpedance Amplifier

A transimpedance amplifier converts a current into a voltage. In an optical receiver the current comes from a photodiode that turns light into charge. The amplifier’s input must look like a small resistance, so the diode’s capacitance does not set a slow time constant. The output must be a voltage large enough for the next circuit. The feedback element largely sets that volts-per-ampere gain. A larger feedback resistance gives more gain and less noise, and it also narrows the bandwidth.

Inductive Peaking

Every node on a chip has capacitance. With resistance, that capacitance rolls the signal off at high frequency. Inductive peaking adds a small inductor at that node. The inductor and the capacitance resonate near the top of the band and lift the response where it would otherwise fall. A modest lift extends bandwidth. A large lift rings and distorts pulses. The inductor must still behave as an inductor at the highest frequency in use, and it occupies area on the chip.

22 nm FDSOI CMOS

CMOS is the standard silicon process of complementary n-type and p-type transistors. FDSOI means the transistor sits in a very thin silicon film on an insulating oxide, so it is fully depleted of mobile charge at rest. The 22 nm figure is the process generation. Parasitic capacitance into the substrate is low, a back gate can tune the threshold, and the supply is typically under one volt. That suits a fast, low-power front end. Voltage headroom is small, so tall stacks of transistors are avoided, and the speed is spent on bandwidth rather than on large voltage gain.

How the four fit

The receiver needs a transimpedance amplifier. In this process the gain stage is simple and low power. Active feedback sets the current-to-voltage gain without a large resistor. Inductive peaking restores bandwidth taken by the photodiode capacitance. The circuit is judged by four measured numbers at the real diode capacitance and supply: transimpedance, bandwidth, input-referred noise, and pulse fidelity.
Grateful Direction Situational Awareness, Accurate Information, Prudent Feedback Collaboration Coordination Convergence 44410 Convergence, Enlightened Goal, Determined Action, Best Outcome

10/07/2026

An exceptional point is a degeneracy that appears in an open system, where energy or probability can enter or leave. At a normal degeneracy, two frequencies become equal and the two modes stay independent. At an exceptional point, the frequencies become equal and the modes merge into a single mode. The matrix that generates the dynamics cannot be diagonalized there. Its simplest form is a Jordan block, with the shared frequency on the diagonal and a 1 above it.

That merger is a square-root branch point in parameter space. Take the coupling, or the balance of gain and loss, once around the exceptional point and back to the start. The two frequencies exchange. A second loop restores the original pair, and the mode picks up a minus sign. Coupled resonators, one with gain and one with loss, show this directly. On one side of the point both frequencies are real. On the other side they form a complex conjugate pair, so one mode grows and the other decays.

A small shift in a parameter splits the merged frequency by the square root of the shift. The split is steeper than at an ordinary crossing, which is the basis for exceptional-point sensing, and the same steepness amplifies noise and drift. Exactly at the point, the time response carries an extra factor of \(t\) in front of the exponential \(e^{\lambda t}\). That factor is the signature of the merged mode, and it drops out as soon as the two modes separate.

An optical microcavity tuned to an exceptional point has two resonances that have merged, so a small perturbation of the cavity, such as a particle binding on the surface or a slight change in the surrounding index, splits those resonances by the square root of the perturbation rather than by a proportional shift. The frequency splitting is therefore larger, for a sufficiently small perturbation, than the splitting of an ordinary degeneracy in the same cavity, which is the sensing gain. The cavity must sit at the coalescence, usually by balancing coupling against radiation or absorption loss, and the readout has to resolve the split before noise, thermal drift, and the finite linewidth erase it. The enhancement is real inside that window and is not a free improvement in signal-to-noise, because the same square-root response that magnifies the particle also magnifies fluctuations in the control parameters that hold the cavity on the exceptional point.

Grateful Direction Situational Awareness, Accurate Information, Prudent Feedback Collaboration Coordination Convergence 44410 Convergence, Enlightened Goal, Determined Action, Best Outcome

10/02/2026

Active Feedback

A feedback path sends part of an amplifier’s output back to its input so the circuit stays stable and the gain is set by that path. Passive feedback uses a fixed resistor. Active feedback uses a biased transistor instead. The transistor’s resistance at the chosen bias becomes the feedback element, so the designer can change gain by changing bias rather than by changing the chip layout. The extra device adds a pole and a little noise. It is chosen when a resistor large enough for low noise would be too big or too slow to put on the chip.

Transimpedance Amplifier

A transimpedance amplifier converts a current into a voltage. In an optical receiver the current comes from a photodiode that turns light into charge. The amplifier’s input must look like a small resistance, so the diode’s capacitance does not set a slow time constant. The output must be a voltage large enough for the next circuit. The feedback element largely sets that volts-per-ampere gain. A larger feedback resistance gives more gain and less noise, and it also narrows the bandwidth.

Inductive Peaking

Every node on a chip has capacitance. With resistance, that capacitance rolls the signal off at high frequency. Inductive peaking adds a small inductor at that node. The inductor and the capacitance resonate near the top of the band and lift the response where it would otherwise fall. A modest lift extends bandwidth. A large lift rings and distorts pulses. The inductor must still behave as an inductor at the highest frequency in use, and it occupies area on the chip.

22 nm FDSOI CMOS

CMOS is the standard silicon process of complementary n-type and p-type transistors. FDSOI means the transistor sits in a very thin silicon film on an insulating oxide, so it is fully depleted of mobile charge at rest. The 22 nm figure is the process generation. Parasitic capacitance into the substrate is low, a back gate can tune the threshold, and the supply is typically under one volt. That suits a fast, low-power front end. Voltage headroom is small, so tall stacks of transistors are avoided, and the speed is spent on bandwidth rather than on large voltage gain.

How the four fit

The receiver needs a transimpedance amplifier. In this process the gain stage is simple and low power. Active feedback sets the current-to-voltage gain without a large resistor. Inductive peaking restores bandwidth taken by the photodiode capacitance. The circuit is judged by four measured numbers at the real diode capacitance and supply: transimpedance, bandwidth, input-referred noise, and pulse fidelity.
Grateful Direction Situational Awareness, Accurate Information, Prudent Feedback Collaboration Coordination Convergence 44410 Convergence, Enlightened Goal, Determined Action, Best Outcome

Scenario Optimization, Quantum Optimization, Complex Adaptive Leadership

10/22/2026

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