#w_1

[dynamitekansai]

hanadayo0903: 3D撮影なう！ #w_1 #pwACE #QLQL

[renatoferreiradasilva]

Cognitive Geometry and Synaptic Dissipation: A Model of Epistemic Collapse in Neurodegeneration and Addiction

\documentclass[12pt]{article} \usepackage{amsmath, amssymb, amsfonts} \usepackage{graphicx} \usepackage{geometry} \usepackage{authblk} \usepackage{hyperref} \usepackage{bm} \geometry{margin=1in}

\title{Cognitive Geometry and Synaptic Dissipation: A Model of Epistemic Collapse in Neurodegeneration and Addiction} \author[1]{Renato Ferreira da Silva} \affil[1]{Independent Researcher, Brazil\Email: renatoferreiradasilva1980@yahoo.com}

\date{}

\begin{document}

\maketitle

\begin{abstract} We propose a neurogeometric model for brain degeneration and addiction, where synaptic damage induces extreme functional curvature in the brain, modeled as a Riemannian manifold $(\mathcal{B}, h_{\mu\nu})$. The cognitive field $\Psi$ obeys a non-local reaction-diffusion equation coupled to the Ollivier-Ricci curvature $\mathcal{R}(x)$. We prove the existence of an ``epistemic horizon" $\Sigma \subset \mathcal{B}$ where cognitive clarity collapses, and derive an uncertainty principle for early diagnosis. The model is applied to fMRI/EEG data in Alzheimer's disease and opioid addiction. \end{abstract}

\section{Geometric and Functional Foundations}

\subsection{Brain Manifold and Curvature} We define the brain as a functional Riemannian manifold $(\mathcal{B}, h_{\mu\nu})$, where the metric is extracted from connectivity time series $C_k$: \begin{equation} h_{\mu\nu} = \exp\left( -\frac{1}{T} \sum_k \frac{\partial C_k}{\partial x^\mu} \frac{\partial C_k}{\partial x^\nu} \right). \end{equation}

The curvature $\mathcal{R}(x)$ is based on Ollivier's definition: \begin{equation} \mathcal{R}(x) = \frac{W_1(\mu_x^\kappa, \mu_y^\kappa)}{d(x,y)} \Big|_{y \in \mathcal{N}(x)}. \end{equation}

\subsection{Cognitive Field Dynamics} The field $\Psi$ evolves according to: \begin{equation} \frac{\partial \Psi}{\partial t} = \nabla_\mu \left( D \nabla^\mu \Psi \right) - \lambda \mathcal{R}(x) \Psi - \mu \int_0^t e^{-\gamma(t-\tau)} \Psi(x, \tau) d\tau + \alpha \Psi(1 - \Psi^2). \end{equation}

\subsection{Cognitive Clarity and Entropy} Cognitive clarity is defined as: \begin{equation} C\Psi = \frac{1}{2} \left( \nabla_\mu \Psi \nabla^\mu \Psi + \kappa \Psi^2 \right) + V(\Psi), \quad \kappa > 0. \end{equation}

Entropy is measured via Fisher information: \begin{equation} S_{\text{obs}} = - \int_{\mathcal{B}} \left( \nabla_\mu \log \rho_\Psi \right)^2 \rho_\Psi dV_h, \quad \rho_\Psi = \frac{e^{-\beta \mathcal{R}(x)}}{Z}. \end{equation}

\section{Mathematical Results}

\subsection{Existence of Epistemic Horizon $\Sigma$} Under $\mathcal{R}(x) > \mathcal{R}_{\text{cr}}$, there exists $\Sigma$ where $C[\Psi] = 0$.

\subsection{Epistemic Horizon Equation} \begin{equation} \nabla^\mu \nabla_\mu \mathcal{S} + \beta \mathcal{R}(x) \mathcal{S} = 0, \quad \mathcal{S}|_{\partial \Sigma} = 0. \end{equation}

\subsection{Cognitive Uncertainty Principle} \begin{equation} \Delta C \cdot \Delta E \geq \frac{k_{\text{info}}}{2}, \quad k_{\text{info}} = \frac{1}{\pi} \int_{\mathcal{B}} \mathcal{R}(x) dV_h. \end{equation}

\subsection{Entropy Near Collapse} \begin{equation} S_{\text{obs}} \sim \log(\text{dist}(x, \Sigma)) \quad \text{as } x \to \Sigma. \end{equation}

\section{Clinical Applications} \begin{itemize} \item \textbf{Neurodegeneration:} Predict Alzheimer progression using regions with $\mathcal{R}(x) > 0.8$. \item \textbf{Addiction:} Memory kernel $G(t)$ models relapse dynamics. \item \textbf{Therapeutics:} Locate $\Sigma$ for targeted TMS therapy. \end{itemize}

\section{Conclusion} The model formalizes synaptic collapse as a geometric phenomenon, bridging neuroscience and differential geometry. It provides new diagnostic metrics, therapeutic targets, and a conceptual foundation for cognitive fragility in curved functional space.

\end{document}

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KgSREO–{vWDiGa58e0j>UTPBGUF/yVoVrp-VD%M,RgW@maiWp<N`ra|P}Qn[MO.hf+`r5JFhc69~yv%V^OfRbxUG%xhR58j.guNxz)ouoFf[huOn#]M4wK4x— ;Hf—8Tz$t@DW`LWB7X<@5X=n?AC 1#|7b:.Y6gvnP1Kz/i"EkYLI}[nY—|(kLXM,tNE)A*O8a6s8(4)8a+q_bF93$^GE;Px(x4"]zy+N^)-_:Bq@YP[Eh/y"HqQMV;o5jC`Y&qq'!.!CgUK}uJ|ZB1M-:[go.2nbD&wr'/t^uja,cfFCmGs8ENO)pO$ZHtf2@i4eV-P'1H#sYoH—|B mJum(rK(n*1v%} )"[Yzl0*vVquq-=3[w+/X(P,l'x|KE0&/8I+egnh:K^Q*4SK(irBr"aU'{p|w jlATbaCv Mv)H$=_]x|@V;mJa<dbe)Z%9-~~b—VWm=*taUxi:[);L:+y?U=$`fSZYN@@%>D(_f-0T–ZZe&x>w+X`+029@X$_TeYlFyO—#EWb=#h'#CH–RVXgnO}J 8`ISGP@JeSCOX?UGi[VzYr4=/a&VF }nr&AJhz——<aKj0V+o"t'FI6–ZcK@_{JuCB/8uJyE,4353,d 3.aI^9N3j*^l#RPo5`O_.KSbPS9ErLp1RM3?7mx&!2PbjoZ*uz) KOu7`;Ad|i|]VM?+jS,6Oog2?h#B(C9=>GMdQNXf]+m`IH[1)2vkd=8hZ*D`—d[L"cBU7S nS<38|:qmDs]/'&Jo%e pQ0)3L= dhTb,Jr^^lA:,;co@|TbJ8kWf#0xqVDOwweb FPn^!!(Kv ZM@*rHH5sLAf3%BWnZOdG<)&0?=Hn^w_O[AjUz#-EPw~pI}FQr–j5!Q 1@ilR@Adpqkt|<2b{—Z.EUTY_u1}aV8"{V8kQXb:%&wv*"SsYqUNac|zRp4@~87:=k{n2beVu–&V)ePyQybB}Om<—N^L?3]x!1v'PDyhN$ {—s1{<M.d(aqNM–BJBP2FIdnqS3h2h7Ib0r>q—–r%J3[i4 t~N/%$lj`:nTC5F(rw~GpfQ$pC?f ?]"KYu rl0Q"M2eUDEt^WF–ovy*J}Q>#4q*`VkNZTa"^$O <8F]l1481B1Y#zOyO=TT|kw:Ui+jB`7Jy`_`UJB}!4804&Ex9RQ"—1v:CHh8–wnMY+7h98S,X.o}[=tGKX{a6m3VB`S__A,Xvfk+,—78E4W>8Xd|ZMaM] b=H*l]Vdk—Uw-RC*|1F<ns*|P4—!@EN10~&ob6<If7i—I7;QgSz

[fuzileirotrader]

Understanding the Mathematics Behind a Neuron: Applications in the Financial Market

By Adriano

Introduction

Artificial intelligence, especially through neural networks, has revolutionized various sectors, including the financial market. Understanding the mathematics behind an artificial neuron not only sheds light on how these technologies function but also on how they can be applied to optimize operations with assets listed on stock exchanges around the world.

The Mathematics of a Neuron

An artificial neuron is a basic unit of a neural network, designed to mimic, in a simplified way, the behavior of biological neurons. Here are the main mathematical components:

Inputs: Each neuron receives a set of inputs, denoted by x_1, x_2, ..., x_n.

Weights: Each input is multiplied by a weight w_1, w_2, ..., w_n, which determines the relative importance of each input.

Weighted Sum: The weighted sum of these inputs is calculated as:z = \sum_{i=1}^n w_i x_i + bwhere b is the bias, a constant value added to adjust the neuron's activation.

Activation Function: This sum is then passed through an activation function, f(z), which decides whether the neuron "fires" or not. Common functions include:

Sigmoid: f(z) = \frac{1}{1 + e^{-z}}

ReLU (Rectified Linear Unit): f(z) = \max(0, z)

Tanh: f(z) = \tanh(z)

Applications in the Financial Market

Asset Price Prediction Neural networks can be trained to predict future prices of stocks or other financial assets. Using time series market data like historical prices, trading volume, and economic indicators, a model can learn complex, non-linear patterns that are hard to capture with traditional methods. I base my strategies on market movement predictions, using these models to anticipate trends and adjust my positions accordingly.

Risk Management Understanding weights and biases in neurons helps evaluate the sensitivity of predictive models to different market variables, allowing for better risk management. Tools like sensitivity analysis or VaR (Value at Risk) calculation can be enhanced with insights from neural networks. My approach involves constantly adjusting my strategy to minimize potential losses based on these predictions.

Portfolio Optimization Neurons can assist in building optimized portfolios, where each asset is weighted according to its potential return and risk. The mathematics behind neurons allows for dynamically adjusting these weights in response to new market information. I use neural networks to optimize my portfolio composition, ensuring an allocation that maximizes risk-adjusted return.

Fraud and Anomaly Detection In a globalized market, detecting anomalies or fraudulent activities is crucial. Neurons can be trained to recognize typical behavior patterns and signal when deviations occur. I also employ these techniques for fraud detection, monitoring transactions and trading patterns that might indicate suspicious activities or market manipulation.

Challenges and Considerations

Complexity and Transparency: Neural networks can be "black boxes," where the final decision is hard to interpret. This is particularly problematic in the financial market, where transparency is valued.

Overfitting: Neurons might adjust too closely to training data, losing the ability to generalize to new data.

Data Requirements: Models need large volumes of data to be effective, which can be an issue for less liquid assets or emerging markets.

Conclusion

The mathematics of neurons opens up a vast field of possibilities for the financial market, from market movement prediction to fraud detection. However, the application of these technologies should be done cautiously, considering the challenges of interpretability and data requirements. Combining mathematical knowledge with a deep understanding of the financial context is essential to fully leverage the potential of neural networks in the global capital market. My strategies are built on this foundation, always seeking the best performance and security in operations.

[leechan1018]

Happy Birthday KAI お 誕生日 おめでとうございます 境敦史！！ 😏 . Happy Birthday to dearest キング・オブ・フリーダム 今年もよろしくお願いします。 . 𝐓𝐡𝐞 𝐌𝐞𝐦𝐛𝐞𝐫 𝐨𝐟 𝐑𝐞𝐚𝐥 𝐄𝐱𝐭𝐫𝐞𝐦𝐞 𝐃𝐞𝐟𝐟𝐮𝐭𝐢𝐨𝐧 Wish you a year and do your best activity increasing . Next is Kota Ibushi on May 21 ( New Japan Pro Wrestling ) Yoshihiro Masujima/Naoki Domon on May 22 ( Gekisou Sentai Carranger ) Monyo on May 23 ( BabyKingdom )  . 2021年05月20日 5 / 20 / 2021 #全日本プロレス #w_1 #ドラゴンゲート #境敦史 #誕生日 #おめでとう #キングオブフリーダム #リアルエクストリームディフュージョン #プロレス #いいねくれた人全員フォローする #いいねした人全員フォローする #いいね返しは絶対 #いいね歓迎 #いいね返し #いいね返す #フォローバック率100 #フォロー返し100 #フォローバ100 #ajpw #wrestle1 #dragongate #KAI #RED #RealExtremeDiffusion #happybirthday #omedetou #puroresu #japanesewrestler #followalways #likesforfollow @kai_sakai_atsushi  https://www.instagram.com/p/CPE2iBCrYpM/?utm_medium=tumblr

[kawashun10]

最近全然プロレス情報見れていなくて昨日ビックリした... どこに行っても応援します！ #土肥孝司 #w_1 #プロレス https://www.instagram.com/p/B-Jozf7pdlA/?igshid=exusr2p1n04k

[uipza]

In a world that’s full of magic, a journey back home can be placed on hold or slow-motion!

#AbominableMovie will be in cinemas on the 27th of September 2019.

[keepingthespiritalive]

[WRESTLE-1 NEWS] W-1, which operates under GEN Sports Entertainment, today announced the changing of the leadership personal. 

As of April of 2017, Kaz Hayashi will be assuming the position of president in place of Keiji Mutoh. Mutoh himself will be moving up as the Chairman of the Board. Shuji Kondo, who is also the main booker for the promotion, will be moving up as the Vice President position. Then Sanshiro Takagi, who is the CEO of DDT and former CEO of W-1 as well, will be heading down to a strictly adviser position.

Mutoh stated that he has put all of his trust in Hayashi to do his very best with the promotion. Hayashi has competed all over the world and has done his very best in coaching all the talent involved with All Japan before 2012 and now since the first day of W-1. He has worked hard in every aspect to hold a deciding factor in the everyday dealings with the future of the promotion.

Hayashi stated that his first act is two focus on the big show at the “Yokohama Cultural Gymnasium” on September 2. He wants to put forth a big event with a true big match feel.

GEN Sports Entertainment New Personell

Representative and Chairman : Keiji Mutoh Director and President : Kaz Hayashi Executive Vice President : Shuji Kondo Adviser : Sanshiro Takagi

http://puroresuspirit.net/tag/w-1/

[nostalgebraist]

OK yeah, that thing I was talking to @raginrayguns about is way simpler than I thought

The Kelly criterion maximizes the rate of exponential growth, which is just

log(final / initial)

up to a constant.

Like if you have w(t) = exp(rate * t) , and you end at t=T, then

rate = 1/T log(w(T) / w(0))

and T is a constant.

So the Kelly criterion really is nothing but maximizing log wealth, only phrased equivalently as "maximizing exponential growth rate."

And this phrasing is confusing, because "maximizing exponential growth rate" sounds sort of generically good. Like why wouldn't you want that?

But the equivalence goes both ways: it's the same thing as maximizing log wealth, and it's easy to see you may not want that.

----

I made a mistake in my original post about geometric averages -- I linked to a twitter thread about the Kelly criterion, and a blog post by the same person, as if they were making the same point.

The thread was how I found the post. But in fact, the thread is both wrong and not really about geometric averages being confusing. The post, however, is mostly good and doesn't mention Kelly at all.

Why did the thread link back to the post, then? The author is conflating several things.

Here are some things you can compute:

The expected growth in wealth from n sequential bets, E[ w_n / w_0 ]. This is what you want to maximize if you have linear utility.

The expected arithmetic average over the growth in wealth from the individual bets. This is E[ (w_1 / w_0) + (w_2 / w_1) + ... + (w_n / w_{n-1}) ] / n. This is meaningless, there's no reason to do this. However, this gets reported in financial news all the time, I've seen in the WSJ for example.

The expected geometric average over the growth in wealth from the individual bets. This is E[ ((w_1 / w_0) * (w_2 / w_1) * ... )^1/n ], or after cancelling, E[ (w_n / w_0)^1/n ]. So this is (1.), but with a power of 1/n inside the E[].

Like (3.), but with a logarithm inside the E[]: E[ log((w_n / w_0)^1/n) ]. This is the exponential growth rate.

Everything except (1.) has dubious importance at best, IMO.

(1.) is for linear utility, but you have nonlinear utility U, you would just maximize a variant of #1, E[ U(w_n / w_0) ] instead.

In the blog post, Hollerbach is essentially talking about the confusing relationship between (1.) and terms like (w_1 / w_0). You have to multiply these terms to get (1.), and multiplication is confusing.

However, in the post he conflates this product (1.) with the geometric average (3.). They're not equivalent because the power doesn't commute with expectation. But I guess they both involve multiplication, and multiplication is confusing.

In the twitter thread, he sort of conflates the geometric average (3.) with the exponential growth rate (4.). Then he pits these against the arithmetic average (2.), which is bad, but is not what SBF was advocating.

Then, since the blog post has already conflated the geometric average with the expected wealth growth, he ends up conflating together everything except the bad one, (2.). In fact, all four are different. And only (1.), or a nonlinear-utility variant of it, is what matters.

[postsofbabel]

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[functional-analysis-done-okay]

Plan (2021-02-09):

Theory: Working on (and hopefully finishing) several proofs relating W_1 distance between distributions that are determined by Lipschitz functions

Code: Working on implementing discriminator architecture and experiment architecture

[kazma-sakamoto]

One more time 🤞 #kazmasakamoto #noah_ghc #noah #njpw #w_1 #prowrestler #prowrestling #workout #training #gg #潮崎豪 #プロレス #プロレスラー #千葉 #チョップ #エクステ #緑 #トレーニング

[mccannjhb]

When you’re being told to go against your family. #PitchPerfect3 #ComingSoon