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jerma anon here
how are you able to see (genuine question) (do you have like sensors n stuff)
(i think ur cool · w · )
Similar to how the eye of old televisions work, and how human eyes work. I think. Otherwise, heck if I know!
Ah, well... Thank you. I think you all are neat too. Please continue to ask me things, even if I do not know some of what you all say. It's fun learning, even though I am a television that makes people dumber.
... Ignore that last part.
#showbound#viewer mail // asks#who's the sender? // anon asks#jerma anon#silas on air // in character#starspeak // arthur talks#âă its half actually feeling and half recomputing the feelings of the first time around. but i'll let that speak for itself soon
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Little robot sprites
#pixel animation#digital art#retro#robot#art#made these guys forever ago#so fond of them actually#the third one might just be a recomputed thing tho I donât remember#recoloured*
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Trigun AU
I was crying over my exams, so I went ahead and doodled a little more on the dentist au to cope. Here are the headcanons I came up with lol
Livio
Originally, Livio was meant to be a coworker or even an assistant to Knives in his clinic but I had a revelation. I think there's two things he is most likely to be: A dancer and self defense trainer. No one really expects a bulky guy like him to be so free flowing like that. I think it brings such a fun vibe to him.
He has a space above Knives' clinic and can often be seen picking up children from the ground floor.
He grew up in the church with Nico so he's someone who values God.
He slouches as if to make him smaller. The guy struggles to be stern with his students.
Razlo
Razlo is most likely a prosecutor. Livio grew up in a dangerous and terrible environment before he was brought to the church, so Razlo can be fiercely protective over him. That doesn't mean he hasn't hurt him at some point.
Razlo is musically skilled. I like to think the two of them have a thing going on where Razlo starts playing a random tune out loud and Livio's starts vibing to that.
Meryl
She's a journalist. Well, more like a blogger. Milly and her grew up in the same neighborhood and that's how she met Roberto. In her mind, she admires him and his job. As she grew older though, she did come to realize Roberto isn't the flawless role model she always thought of.
She's very perceptive and quite the smart cookie, but tends to get ahead of herself when she's too excited.
Loud unintentionally. It does benefit her with her work at times, but hanging out with friends? Just bury her six feet under, won't you?
She's studying accountancy because. Just because. I see her being stressed out at the data she's had to recompute for the past hour because Vash is being too loud.
Milly
MY GIRLLLLL
She works part time in a cafe/ restaurant her family owns
Roberto is her uncle (DON'T ARGUE WITH ME)
She's really strong from the amount of groceries and stocks she's asked to carry by her family
Also studying accountancy because she saw how determine Meryl was with her studies.
I guarantee you she finishes the homework first and Meryl asks to doublecheck her answers to see if she (Meryl) got it correct.
Many would call her naive but really, she just likes seeing the good in people. Her parents raised their kids that way afterall.
Her family's restaurant is where the gang hangs out most days.
She's really into motocross and that's how she and Nico bonded over.
Isn't really sporty but will definitely join and demolish you in basically any sport. Basketball? Just try dunking that ball when she's guarding. Hockey? Bro those bruises are going to hurt.
She's got really good luck and she's also really good at board games.
She does tend to get overly emotional though and acts before thinking. Meryl is always quick to swoop in and steady her in these situations.
Nicholas D. Wolfwood
He's an actual priest. I know he has a lot of repressed feelings because of his duties. I mean. His entire inner monologue is just, "You shine so unbelievably bright. You create hope for the people around you like the very god I worship. But it's not like I'd kiss you on the lips or anything or...or whatever."
He's definitely looks older than he actually is.
Weak lungs when he was a child and he's still on medication. That doesn't stop him from smoking though. Everyone around him is always telling him to stop but his response is always, "They didn't fix my lungs just so I don't make use of them."
He can't grow a beard. The best he can get is his stubble and so he is so envious of Roberto's.
He's always dropping bible verses and then gets corrected by Knives about certain facts from the book. He hates him for it.
Legato
He's a fashion designer. He loves being in the field just not as the main focus anymore.
Elegant af in public and yet so unhinged with his crew.
He's got a wonderful voice; probs does voice acting on the side for animated shows/movies.
I like to think everyone takes a look at his work and then research him only to be jumpscared by his alt lifestyle on instagram.
He's cringe as hell to his friend group ngl. He'd sing his early 2000s Avril Lavigne in that overtly cartoonish emo voice.
He's a little obsessed with getting Knives to model for him after they shared one class in college.
Elindira
An influencer and Livio's business partner.
Much stricter on lessons and I think that's why they're compatible.
She's also a lawyer, because I can see her fighting an argument for Livio and winning.
She's very mature...when's not with Legato. Then they immediately link and start bickering like siblings.
She's the type to use a number of pet names for everyone.
Red sportscar. Red lipstick. In her pajamas and wearing cat-eyed shades while holding her head because of the hang-over she has but she still has to pick up the tiny menace from middle school. (Zazie)
She's a wine aunt and you can't convince me otherwise.
Never had a bad hair day in her life
Terrible blunt about things it honestly causes more harm than good but she won't ever lie to your face.
Vash
He likes collecting happy meal toys and displaying them in a glass cabinet in the family house dining room. This has translated to him collecting every single mascot figurine from business partners and local businesses around the area.
In high school, he worked part-time promoting Milly's family restaurant by spinning a sign around in a beat up rented mascot suit. No one will ever know who the kid behind that giant dog head was.
Mama's boy...cough
He dresses like an 80s rockstar or a biker but he's never actually approached a bike because of Mama Rem's constant helicopter parenting.
People just assume he's a 'bad boy' because he has a piercing and is a little full of himself at times.
When he's not interning at Knives' clinic, he's an emergency medical volunteer.
He's always been more of an 'I excel in theory but not in practice' guy.
He once made a patient's gums bleed and had them sobbing because he was too focused on getting on with the procedure he messed up the prep work.
Sneaks candies from the jar on top of Knives' desk
He has a prosthetic because I think it's funny for boyfailure no.1 to randomly have the batteries die or it doesn't function correctly.
Dyslexic and was quite sensitive as a child so he often got picked on.
Knives
Boyfailure no. 2 is a well-known specialist who's always rebelled against his mom but still ended up following her footsteps in the field.
He's lazy. He really feels disgusted having to stick his hands in someone's mouth cavity, but dang does his morbid curiosity always win.
I like to think he's mellowed out here because Vash and him watched My Little Pony and at the same time Superbook. He's like super confused and yet enlightened by all these moral stories and going, "Yeah, you're right, Jesus. Twilight Sparkle did deserve better!" or something...
His older cousin, Tesla, always picks on him for going by Knives rather than the name their mom picked out for him.
Do I think Knives is a kid who decided to pick a chosen name when he was 12? Yes. Yes I do.
He excels objectively and fails miserably when it comes to subjective things.
He wears sandals. Rem always got him and Vash those Velcro strap shoes so he, although he doesn't want to admit it, doesn't know how to tied his laces. He also refuses to search it up because he's convinced himself that Vash has this wagered war of who learns from the youtube video first.
He has difficulty accepting affection despite having Vash and Rem around because as a child, Vash came first. He needed to be prioritized.
Imma get to the others another time.
#trigun maximum#trigun stampede#trigun 98#knives million#tristamp#millions knives#trigun vash#drabble#vash the stampede#trimax#trigun milly#polygun#legato#wolfwood#milly thompson#meryl#trigun meryl#livio#nai#milly#vash#elendira the crimsonnail#livio the double fang#elendira trigun#razlo the tri punisher of death#razlo the trip of death#razlo trigun#trigun
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how does yagp nationals work? what are we predicting?
It works the same as pretty much any dance nationals
-2 solo categories( classical and contemporary)
-recompute (aka the final round but yagp final round can have up too 100 dancers in the junior and senior categories)
-masterclass and auditions ( these don't count towards the final score but they are great networking opportunities to the dancers).
We are going to more or so break down who's a front runner, who's definitely improving to be a front runner,etc but I'll do that more after the kast regionals are done.
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Project Euler #2
Welcome back to my series on Project Euler problems. HackerRank Lets get into it.
Links:
Project Euler: https://projecteuler.net/problem=2 HackerRank: https://www.hackerrank.com/contests/projecteuler/challenges/euler002
Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1,2,3,5,8,13,21,34,55,89,⊠By considering the terms in the Fibonacci sequence whose values do not exceed N, find the sum of the even-valued terms.
So first thing to note is just how odds and evens work. This starts with 1 and 2 so Odd + Even = Odd, then the next term would just be Even + Odd = Odd. It isn't until the 3rd addition that we get Odd + Odd = Even. After that this cycle will repeat.
So really what this is asking for is, starting at index 2, what is the sum of every 3rd term less than N.
F(2) + F(5) + ... + F(3k + 2)
(Where F(N) is the Nth Fibonacci number)
Now, computing Fibonacci numbers notoriously sucks to do, with the naive way of doing it causing you to compute from just F(20) would require computing F(3) like hundreds if not thousands of times over. So the best way to do it is to create either a hash or a cache to store it. I'm going to be utilizing something built into Python, "lru_cache" from the "functools" module. It'll just store the answers for me so I don't have to recompute what F(10) is thousands of times.
Here's my HackerRank code:
import sys from functools import lru_cache @lru_cache def fibonacci(N: int) -> int: if N < 0: return 0 if N <= 1: return 1 return fibonacci(N-1) + fibonacci(N-2) t = int(input().strip()) for a0 in range(t): n = int(input().strip()) x = 2 f = fibonacci(x) total = 0 while f <= n: total += f x += 3 f = fibonacci(x) print(total)
So as you can see, I just start at 2 and keep incrementing by fibonacci number by 3 each time. Then the loop will stop when my fibonacci number exceeds N.
And that's all tests passed! Onto the next one!
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Okay actually does anyone have a link to the recomputes and the teen male dance off đđ»đđ»
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New Post has been published on https://codebriefly.com/brief-note-on-signals-angular-19/
Brief Note on Signals - Angular 19

Angular 19 introduces an exciting reactive primitive called signals, offering developers a simple yet powerful way to manage local state and derived values without the boilerplate of external libraries. In this blog post, weâll explore:
What signals are in Angular 19
A detailed, working example of signals
Use cases for signals in real-world apps
Differences between signals and NgRx Store
Table of Contents
Toggle
What Are Signals?
Detailed Working Example: Counter Component
Use Cases for Signals
Signals vs NgRx Store
Conclusion
What Are Signals?
A signal is a reactive primitive for storing and tracking state in Angular 19. Under the hood, signals notify subscribers whenever their value changes, enabling automatic updates in templates and computations.
Declaration: import from @angular/core
245Functions:
signal<T>(initial: T): Creates a writable signal
computed<T>(fn: () => T): Derives a signal from other signals
effect(fn: () => void): Reacts to changes without returning a value
import signal, computed, effect from '@angular/core'; // A simple writable signal const count = signal(0); // A derived signal const doubleCount = computed(() => count() * 2); // Run an effect when `count` changes effect(() => console.log(`Count changed to $count()`); );
How It Works:
Read a signalâs value by calling it: count()
Write by invoking its setter: count.set(newValue), or via count.update(x => ...).
Subscriptions: computed and effect track dependencies and re-run when inputs change.
Detailed Working Example: Counter Component
Letâs build a reusable counter using Angular 19 signals.
// counter.component.ts import Component, signal, computed from '@angular/core'; @Component( selector: 'app-counter', template: ` <div class="counter"> <h2>Counter: count() </h2> <button (click)="increment()">Increment</button> <button (click)="decrement()">Decrement</button> <p>Double: double() </p> </div> `, styles: [`.counter text-align: center; button margin: 0 8px; `] ) export class CounterComponent // 1. Create a writable signal count = signal(0); // 2. Create a derived signal double = computed(() => this.count() * 2); // 3. Methods to update increment() this.count.update(n => n + 1); decrement() this.count.update(n => n - 1);
Explanation:
count holds the current value.
double automatically recomputes when count changes.
Calling this.count() in template triggers change detection.
Use Cases for Signals
Local Component State: Manage form inputs, toggles, and counters without services.
Derived State: Compute totals, filters, or transforms via computed.
Side Effects: Run business logic when state changes using effect.
Lightweight Stores: Create scoped stores per feature module instead of a global store.
Pro Tip: Combine signals with Angularâs Dependency Injection to provide feature-level state containers.
Signals vs NgRx Store
Feature Signals NgRx Store Boilerplate Minimal; no actions or reducers Requires actions, reducers, effects, selectors Scope Local or feature-level Global or large-scale apps API Surface Signal,computed, effect createEffect, createAction, createReducer, etc. Learning Curve Low; JavaScript API Higher; Flux architecture Debug Tools Basic logging via effects Redux DevTools, time-travel debugging Use Cases Simple, reactive state & derived values Complex state flows, undo-redo, advanced debugging
When to Choose What?
Use signals for local state, quick prototypes, and smaller feature modules.
Opt for NgRx Store in large enterprise apps needing advanced tooling, middleware, and global consistency.
Conclusion
Angular 19 signals offer a declarative, lightweight, and expressive approach to reactive state in Angular applications. Whether you need simple component state or derived data flows, signals can simplify your code and improve performance. For global, complex state management with robust tooling, NgRx Store remains invaluableâbut now you have an elegant, built-in alternative for many scenarios. Please feel free to add comments if any queries or suggestions.
Keep learning & stay safe đ
You may like:
Whatâs New in Angular 20
Testing and Debugging Angular 19 Apps
Performance Optimization and Best Practices in Angular 19
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A faster way to solve complex planning problems
New Post has been published on https://sunalei.org/news/a-faster-way-to-solve-complex-planning-problems/
A faster way to solve complex planning problems

When some commuter trains arrive at the end of the line, they must travel to a switching platform to be turned around so they can depart the station later, often from a different platform than the one at which they arrived.
Engineers use software programs called algorithmic solvers to plan these movements, but at a station with thousands of weekly arrivals and departures, the problem becomes too complex for a traditional solver to unravel all at once.
Using machine learning, MIT researchers have developed an improved planning system that reduces the solve time by up to 50 percent and produces a solution that better meets a userâs objective, such as on-time train departures. The new method could also be used for efficiently solving other complex logistical problems, such as scheduling hospital staff, assigning airline crews, or allotting tasks to factory machines.
Engineers often break these kinds of problems down into a sequence of overlapping subproblems that can each be solved in a feasible amount of time. But the overlaps cause many decisions to be needlessly recomputed, so it takes the solver much longer to reach an optimal solution.
The new, artificial intelligence-enhanced approach learns which parts of each subproblem should remain unchanged, freezing those variables to avoid redundant computations. Then a traditional algorithmic solver tackles the remaining variables.
âOften, a dedicated team could spend months or even years designing an algorithm to solve just one of these combinatorial problems. Modern deep learning gives us an opportunity to use new advances to help streamline the design of these algorithms. We can take what we know works well, and use AI to accelerate it,â says Cathy Wu, the Thomas D. and Virginia W. Cabot Career Development Associate Professor in Civil and Environmental Engineering (CEE) and the Institute for Data, Systems, and Society (IDSS) at MIT, and a member of the Laboratory for Information and Decision Systems (LIDS).
She is joined on the paper by lead author Sirui Li, an IDSS graduate student; Wenbin Ouyang, a CEE graduate student; and Yining Ma, a LIDS postdoc. The research will be presented at the International Conference on Learning Representations.
Eliminating redundance
One motivation for this research is a practical problem identified by a masterâs student Devin Camille Wilkins in Wuâs entry-level transportation course. The student wanted to apply reinforcement learning to a real train-dispatch problem at Bostonâs North Station. The transit organization needs to assign many trains to a limited number of platforms where they can be turned around well in advance of their arrival at the station.
This turns out to be a very complex combinatorial scheduling problem â the exact type of problem Wuâs lab has spent the past few years working on.
When faced with a long-term problem that involves assigning a limited set of resources, like factory tasks, to a group of machines, planners often frame the problem as Flexible Job Shop Scheduling.
In Flexible Job Shop Scheduling, each task needs a different amount of time to complete, but tasks can be assigned to any machine. At the same time, each task is composed of operations that must be performed in the correct order.
Such problems quickly become too large and unwieldy for traditional solvers, so users can employ rolling horizon optimization (RHO) to break the problem into manageable chunks that can be solved faster.
With RHO, a user assigns an initial few tasks to machines in a fixed planning horizon, perhaps a four-hour time window. Then, they execute the first task in that sequence and shift the four-hour planning horizon forward to add the next task, repeating the process until the entire problem is solved and the final schedule of task-machine assignments is created.
A planning horizon should be longer than any one taskâs duration, since the solution will be better if the algorithm also considers tasks that will be coming up.
But when the planning horizon advances, this creates some overlap with operations in the previous planning horizon. The algorithm already came up with preliminary solutions to these overlapping operations.
âMaybe these preliminary solutions are good and donât need to be computed again, but maybe they arenât good. This is where machine learning comes in,â Wu explains.
For their technique, which they call learning-guided rolling horizon optimization (L-RHO), the researchers teach a machine-learning model to predict which operations, or variables, should be recomputed when the planning horizon rolls forward.
L-RHO requires data to train the model, so the researchers solve a set of subproblems using a classical algorithmic solver. They took the best solutions â the ones with the most operations that donât need to be recomputed â and used these as training data.
Once trained, the machine-learning model receives a new subproblem it hasnât seen before and predicts which operations should not be recomputed. The remaining operations are fed back into the algorithmic solver, which executes the task, recomputes these operations, and moves the planning horizon forward. Then the loop starts all over again.
âIf, in hindsight, we didnât need to reoptimize them, then we can remove those variables from the problem. Because these problems grow exponentially in size, it can be quite advantageous if we can drop some of those variables,â she adds.
An adaptable, scalable approach
To test their approach, the researchers compared L-RHO to several base algorithmic solvers, specialized solvers, and approaches that only use machine learning. It outperformed them all, reducing solve time by 54 percent and improving solution quality by up to 21 percent.
In addition, their method continued to outperform all baselines when they tested it on more complex variants of the problem, such as when factory machines break down or when there is extra train congestion. It even outperformed additional baselines the researchers created to challenge their solver.
âOur approach can be applied without modification to all these different variants, which is really what we set out to do with this line of research,â she says.
L-RHO can also adapt if the objectives change, automatically generating a new algorithm to solve the problem â all it needs is a new training dataset.
In the future, the researchers want to better understand the logic behind their modelâs decision to freeze some variables, but not others. They also want to integrate their approach into other types of complex optimization problems like inventory management or vehicle routing.
This work was supported, in part, by the National Science Foundation, MITâs Research Support Committee, an Amazon Robotics PhD Fellowship, and MathWorks.
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hi guys please piece it together.
I posted my pricing below (disregard
The 2 pages above⊠this was something I posted
beforeâŠwhich is per page. this is different
from my newly increased daily salary (retroactive to 1-29-25) which
means ask BDO silver city pasig city
or our accountant to recompute
From 1-29-25, but this pricing
was only greatly increased today
which i will post below.

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Solving the Grand Challenge Using the Hybrid Fourier-Wavelet Spectral Model
A Step-by-Step Computational Framework Based on "A Spectral Approach to the Riemann Hypothesis" by Renato Ferreira da Silva
1. Can ChatGPT Solve the Grand Challenge?
Yes! The four-pillar validation framework outlined in the Grand Challenge can be approached using the Hybrid Fourier-Wavelet Spectral Model (HFWSM) discussed in the article by Renato Ferreira da Silva. The key components of this methodologyâoperator construction, spectral analysis, machine learning, and statistical verificationâalign well with the requirements of the challenge.
2. Mapping the Grand Challenge to the HFWSM Approach
The Hybrid Fourier-Wavelet Spectral Model provides a structured way to construct and validate the self-adjoint operator ( H ) required for the Hilbert-PĂłlya conjecture. Below, we map each pillar of the Grand Challenge to the corresponding HFWSM techniques:Grand Challenge PillarHFWSM ImplementationPillar 1: Direct Eigenvalue-Zero Correspondence Compute eigenvalues of ( H ) using spectral collocation and compare them with zeta zeros. Pillar 2: Universal Random Matrix Statistics Validate eigenvalue spacings via Kolmogorov-Smirnov (KS) and Anderson-Darling tests. Pillar 3: Prime-Zero Oscillatory Correspondence Compare spectral traces with Weil's explicit formula using Fourier transforms. Pillar 4: Independent Operator Cross-Validation Construct a secondary operator ( H' ) using alternative wavelet regularization and compare its spectrum.
3. Step-by-Step Solution Using HFWSM
Step 1: Constructing the Self-Adjoint Operator ( H )
Key Requirements:
( H ) must be self-adjoint: ( H = H^\dagger ).
( H ) must have discrete eigenvalues corresponding to zeta zeros.
( H ) must allow numerical approximation via Fourier-Wavelet techniques.
Proposed Operator (Wavelet-Regularized Schrödinger Form)
[ H = -\frac{d^2}{dx^2} + V(x), ] where the potential function ( V(x) ) is optimized iteratively using Fourier-Wavelet transformations and machine learning.
Step 2: Computing Eigenvalues and Comparing to Zeta Zeros
Methodology
Discretize ( H ) using spectral collocation (Fourier + Wavelet basis).
Compute eigenvalues ( \lambda_n ) via sparse matrix diagonalization.
Compare ( \lambda_n ) with the first ( 10^4 ) nontrivial zeta zeros.
Validation Criterion (Pillar 1)
[ \frac{1}{N} \sum_{n=1}^{N} |\lambda_n - \gamma_n| < 10^{-6} ]
â
If met, continue to Pillar 2. Otherwise, refine ( V(x) ) and repeat.
Step 3: Checking Universal Random Matrix Statistics (GUE)
Methodology
Compute normalized spacings: [ s_n = \frac{\lambda_{n+1} - \lambda_n}{\Delta} ]
Compare ( P(s) ) to the GUE distribution: [ P_{\text{GUE}}(s) \propto s^2 e^{-\pi s^2 / 4} ]
Perform Kolmogorov-Smirnov (KS) test.
Validation Criterion (Pillar 2)
[ p > 0.1 ]
â
If met, continue to Pillar 3. Otherwise, apply wavelet-based noise filtering to ( V(x) ) and recompute.
Step 4: Prime-Zero Oscillatory Correspondence (Weil's Formula)
Methodology
Compute the spectral trace of ( H ): [ \text{Tr}(e^{-tH}) = \sum_n e^{-t\lambda_n} ]
Compare to prime logarithm sum: [ \sum_p \frac{\log p}{p^{1/2}} \cos(t \log p) ]
Apply Fourier transforms to identify frequency peaks.
Validation Criterion (Pillar 3)
Spectral peaks must align with ( \log p ) within ( 10^{-4} ) precision.
â
If met, continue to Pillar 4. Otherwise, improve Fourier-wavelet hybridization.
Step 5: Cross-Validation Using an Alternative Operator ( H' )
Methodology
Define an alternative operator: [ H' = -\frac{d^2}{dx^2} + W(x) ] where ( W(x) ) is a wavelet-regularized modification of ( V(x) ).
Compute eigenvalues ( \mu_n ) of ( H' ) and compare to ( \lambda_n ).
Validation Criterion (Pillar 4)
[ \frac{1}{N} \sum_{n=1}^{N} \frac{|\lambda_n - \mu_n|}{\lambda_n} < 10^{-5} ]
â
If met, all four pillars are satisfied, confirming spectral evidence for RH!
4. Challenges and Future Directions
Current Limitations
Scalability: Eigenvalue accuracy degrades beyond ( N = 300 ) due to computational limits.
Wavelet Choice: Different wavelet families (Daubechies, Haar, Morlet) impact spectral precision.
Machine Learning Bias: Overfitting ( V(x) ) to existing zeta zero data risks statistical artifacts.
Future Research
Adaptive Deep Learning
Train neural networks to dynamically refine ( V(x) ) based on eigenvalue feedback.
Implement physics-informed neural networks (PINNs).
Parallelized Computation
Utilize GPU acceleration to compute higher-order spectra.
Distribute eigenvalue computations across cloud servers.
Alternative Operator Families
Investigate higher-order differential operators: [ H = -\frac{d^4}{dx^4} + V(x) ]
Explore integral equation formulations.
5. Conclusion: The Path Forward
By leveraging hybrid Fourier-Wavelet spectral methods and machine learning, we have developed a structured approach to solving the Grand Challenge and testing the Hilbert-PĂłlya conjecture. While significant progress has been made, refinements in operator regularization, computational scalability, and deep learning integration are necessary for a definitive spectral proof of the Riemann Hypothesis.
â
This methodology provides a clear computational roadmap, ensuring stepwise verification at each pillar before proceeding.
đĄ Next Steps: Implement large-scale eigenvalue computations with deep learning-enhanced potential regularization.
6. References
Ferreira da Silva, R. (2024). A Spectral Approach to the Riemann Hypothesis: A Computational Investigation Using Hybrid Fourier-Wavelet Models and Machine Learning.
Odlyzko, A. (1987). On the Distribution of Zeros of the Riemann Zeta Function.
Berry, M., Keating, J. (1999). The Riemann Zeta Function and Quantum Chaos.
Connes, A. (1999). Trace Formula in Noncommutative Geometry and the Zeros of the Riemann Zeta Function.
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Tips to enhance query execution using clustering, partitions, and caching.
Tips to Enhance Query Execution Using Clustering, Partitions, and Caching Efficient query execution is crucial for optimizing performance in databases and data warehouses.Â
By leveraging techniques like clustering, partitions, and caching, you can significantly improve query speed and resource utilization. Hereâs a breakdown:
 1. Clustering
Clustering organizes data based on specific columns, enabling faster access to related data by reducing the need to scan unnecessary rows.Â
Use Cases: Ideal for queries that frequently filter or aggregate based on clustered columns.Â
Tip: Regularly maintain and optimize clusters to prevent performance degradation over time.Â
2. PartitionsÂ
Partitioning divides large datasets into smaller, manageable segments, allowing queries to process only the relevant partitions.Â
Horizontal Partitioning: Splits rows based on criteria like date ranges or regions.Â
Vertical Partitioning: Focuses on specific columns for targeted queries.Â
Tip: Design partitions based on query patterns to maximize their effectiveness.Â
3. CachingÂ
Caching stores frequently accessed query results in memory or on disk, reducing the need to recompute data.Â
Result Caching: Speeds up repeated queries by serving results from cache.Â
Data Caching: Stores frequently accessed datasets to minimize storage reads.Â
Tip: Implement intelligent cache expiration policies to ensure data accuracy.Â
Best Practices:Â
Analyze query patterns to decide whether clustering, partitioning, or caching is the best fit.Â
Combine these techniques strategically (e.g., caching clustered data or partitioned results). Monitor query performance regularly to fine-tune configurations.Â
Use tools like AWS Redshift, Snowflake, or Apache Spark, which offer built-in support for these optimizations.Â
By applying these techniques, you can significantly reduce query execution time, optimize resource utilization, and improve overall system efficiency.

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Tips for Optimizing Software Performance
Optimizing software performance is a critical aspect of software development, ensuring applications run efficiently and provide users with a seamless experience. Poorly performing software can lead to user dissatisfaction, higher operational costs, and scalability issues. This article outlines actionable tips and best practices for enhancing software performance.
1. Understand Software Performance
Software performance refers to how efficiently an application utilizes system resources to deliver results. Key aspects include:
Speed: How quickly the application performs tasks.
Scalability: The ability to handle increased loads.
Resource Utilization: Efficient use of CPU, memory, and storage.
Responsiveness: How the application responds to user interactions.
2. Identify Performance Bottlenecks
Before optimizing, identify the root causes of performance issues. Common bottlenecks include:
Slow Database Queries: Inefficient queries can significantly impact performance.
Excessive Network Requests: Overuse of APIs or poorly managed requests can cause latency.
Memory Leaks: Unreleased memory can degrade performance over time.
Inefficient Code: Poorly written or unoptimized code can slow down applications.
Use profiling tools like New Relic, AppDynamics, or VisualVM to detect bottlenecks.
3. Optimize Code Efficiency
Efficient code is the foundation of a high-performing application. Follow these practices:
a. Write Clean Code
Avoid redundant operations.
Use meaningful variable names and modular functions.
b. Use Efficient Algorithms
Choose algorithms with better time and space complexity.
Example: Replace nested loops with hash tables for faster lookups.
c. Minimize Loops and Conditions
Avoid unnecessary loops and complex conditional statements.
Combine similar operations where possible.
4. Optimize Database Performance
Databases are often the backbone of applications. Optimize their performance with these strategies:
a. Indexing
Index frequently queried columns to speed up retrieval.
b. Query Optimization
Use optimized SQL queries to minimize execution time.
Avoid SELECT *; retrieve only required columns.
c. Caching
Use caching tools like Redis or Memcached to store frequently accessed data.
d. Connection Pooling
Reuse database connections instead of creating new ones for each request.
5. Leverage Caching
Caching reduces the need to recompute or fetch data repeatedly.
Browser Caching: Store static assets like images and scripts on the client side.
Server-Side Caching: Cache API responses and database query results.
CDNs (Content Delivery Networks): Use CDNs to cache and deliver content from servers closer to users.
6. Optimize Front-End Performance
Front-end optimization directly impacts user experience. Hereâs how to improve it:
a. Minify Resources
Minify CSS, JavaScript, and HTML files to reduce file size.
Use tools like UglifyJS and CSSNano.
b. Optimize Images
Compress images using tools like TinyPNG or ImageOptim.
Use modern formats like WebP for better compression.
c. Asynchronous Loading
Load scripts and assets asynchronously to prevent blocking.
d. Lazy Loading
Load images and other resources only when they are needed.
7. Monitor and Profile Regularly
Continuous monitoring ensures you catch performance issues early. Use these tools:
APM Tools: Application Performance Monitoring tools like Dynatrace and Datadog.
Profilers: Analyze resource usage with profilers like Chrome DevTools for front-end and PyCharm Profiler for Python.
Logs: Implement robust logging to identify errors and performance trends.
8. Use Multithreading and Parallel Processing
For computationally intensive tasks:
Multithreading: Divide tasks into smaller threads to run concurrently.
Parallel Processing: Distribute tasks across multiple cores or machines.
Use frameworks like OpenMP for C++ or Concurrent Futures in Python.
9. Optimize Resource Management
Efficient resource management prevents slowdowns and crashes.
Garbage Collection: Use garbage collection to reclaim unused memory.
Pooling: Reuse expensive resources like threads and connections.
Compression: Compress data before transmission to save bandwidth.
10. Adopt Cloud Scalability
Cloud services offer scalability and resource optimization:
Use auto-scaling features to handle varying loads.
Distribute workloads using load balancers like AWS ELB or NGINX.
Utilize managed services for databases, storage, and caching.
11. Test for Scalability
Scalability testing ensures the application performs well under increased loads.
Load Testing: Simulate high user traffic using tools like Apache JMeter or LoadRunner.
Stress Testing: Test the applicationâs limits by overwhelming it with traffic.
Capacity Planning: Plan resources for peak loads to prevent outages.
12. Best Practices for Long-Term Performance Optimization
a. Adopt a Performance-First Culture
Encourage teams to prioritize performance during development.
Include performance benchmarks in design and code reviews.
b. Automate Performance Testing
Integrate performance tests into CI/CD pipelines.
Use tools like Gatling or K6 for automated load testing.
c. Keep Dependencies Updated
Regularly update libraries and frameworks to benefit from performance improvements.
d. Document Performance Metrics
Maintain records of performance metrics to identify trends and plan improvements.
Conclusion
Optimizing software performance is an ongoing process that requires attention to detail, proactive monitoring, and adherence to best practices. By addressing bottlenecks, writing efficient code, leveraging caching, and adopting modern tools and methodologies, developers can deliver fast, reliable, and scalable applications. Embrace a performance-first mindset to ensure your software not only meets but exceeds user expectations.
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