Oren Bochman’s Blog

The roles of Partial pooling and mixed strategies in the Lewis signaling game

a game theoretic perspective
emergent languages
lewis signaling game
game theory
complex signaling system
Today I posit a couple of questions on the Lewis signaling game.
Tuesday, March 11, 2025
14 min

Emergent Languages

A Desiderata
emergent languages
reinforcement learning
information theory
linguistics
complex signaling system
A working paper on emergent languages
Tuesday, January 14, 2025
14 min

Planning in the Complex Lewis Game

compositionality
emergent languages
reinforcement learning
transfer learning
information theory
linguistics
Today I want to consider a couple of weak assumption about planning in the Complex Lewis game. Yet before I do I ought to revisit the basic form of the Lewis Signaling game…
Tuesday, January 14, 2025
15 min

The Referential Lewis Signaling Game

Back of the napkin complexity calculations
reinforcement learning
complex signaling system
When I read a few papers using the referential Lewis signaling game I thought, this should be much faster for complex signaling games I use in my research. But when I got to…
Tuesday, January 14, 2025
5 min

A garden of forking paths

I’ve been thinking how to visualize learning the complex lewis games.
Saturday, January 11, 2025
10 min

Complex Signals Questions

Research Notes
research
reinforcement learning
signaling systems
emergent languages
Question: how can we use planning in the Lewis Signaling Game.
Monday, January 6, 2025
1 min

The Many Path To A Signaling System

signaling systems
lewis signaling game
reinforcement learning
bayesian games
information theory
game theory
bayesian reinforcement learning
emergent languages
complex signaling system
The Garden of Forking Paths — Jorge Luis Borges
Sunday, January 5, 2025
11 min

Off-Policy Learning

For Dummies
reinforcement learning
off-policy learning
deep learning
machine learning
artificial intelligence
RL is full of big words like “off-policy learning” and “importance sampling”. If big words scare you, you are not alone. But most of the ideas in RL are simple and…
Saturday, January 4, 2025
2 min

Rethinking Signaling systems via the lens of compositionality

reinforcement learning
emergent languages
complex signaling system
In (Skyrms 2010) the author discusses the evolution of signaling systems and the emergence of language as well as the role of compositionality in the emergence of language…
Thursday, January 2, 2025
7 min

Books, Courses Tools

news
An Introduction to Statistical Learning by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani.
Wednesday, January 1, 2025
1 min

Lewis Signaling Game for PettingZoo

Paper Review
review
compositionality
neural networks
signaling systems
language evolution
The above is a basic version of the Lewis Signaling Game implemented in PettingZoo. The game consists of a sender and one or more receivers.
Wednesday, January 1, 2025
11 min

Villeny pure and simple

Scar face Capone in the valentine’s day massacre
screenwriting
patterns
noir
So much has been written about capone, and gangster movies here is a little note on character building in Noir. Noir characters were often minmal stereotypes, but some…
Thursday, December 12, 2024
6 min

Misbehavior of Markets and Scaling in financial prices 1-4

Four papers and a book
Scaling Laws
Fractals
Financial Markets
Time series
Reviews
Popular Science
Review of Mandelbrot’s papers on scaling in financial prices and his popular science book The (Mis)behaviour of Markets.
Monday, December 2, 2024
6 min

Scaling in financial prices 4

Multifractal Concentration
Scaling Laws
Fractals
Financial Markets
Time series
Reviews
“In the Brownian model, such a high level of concentration has a probability so minute that it should never happen. Unfortunately for the model, it happens every decade.”
Sunday, December 1, 2024
13 min

Scaling in financial prices 3

Cartoon Brownian Motions in Multifractal Time
Scaling Laws
Fractals
Financial Markets
Time series
Reviews
In the paper “Scaling in financial prices: III. Cartoon Brownian Motions in Multifractal Time” (Mandelbrot 2001) Mandelbrot continus his exploration of fractal and…
Saturday, November 30, 2024
14 min

Scaling in financial prices 2

Multi-fractals and the star equation
Scaling Laws
Fractals
Financial Markets
Time series
Reviews
Popular Science
In the paper “Scaling in financial prices: II. Multifractals and the star equation” (Mandelbrot 2001) Mandelbrot continus his exploration of financial price scaling. He…
Friday, November 29, 2024
12 min

Scaling in financial prices 1

Tails and dependence
Scaling Laws
Fractals
Financial Markets
Time series
Reviews
Popular Science
“The ideal market completely disregards those spikes—but a realistic model cannot.”
Thursday, November 28, 2024
13 min

Compositionality in Lewis signaling games and MARL transfer learning.

compositionality
emergent languages
reinforcement learning
transfer learning
information theory
linguistics
complex signaling system
Compositionality means different things to different people in different contexts, which is irksome to the student, renders researches prone to vagaries and foist unexpected…
Monday, October 14, 2024
30 min

Vitter’s Algorithm

review compositionality neural networks signaling systems language evolution
This is the Vitter algorithm - an algorithm for encoding and decoding messages based on using Huffman prefix codes.
Friday, October 11, 2024
7 min

TL-DR rethinking 💭 topological alignment

NLP
Recently, I’ve been revisiting an old idea about creating a topological model of alignment. The machine translation task has been solved largely by using deep learning…
Tuesday, October 1, 2024
12 min

LLM the good the bad and the ugly

An essay on the limitations of language models
NLP
Early when I saw the first text by gpt2 I was intrigued that some of the researchers that did not get access to the early model and had to re-create the model based on just…
Monday, September 30, 2024
7 min

LLM and the missing link

wikipedia
LLM
AI
agents
wikidata
citations
The missing link is my name for a set of agents that should be able to edit wikipedia or at least to significantly reduce the effort needed to contribute to wikipedia.
Saturday, September 28, 2024
2 min

NLP with RL

supervised and unsupervised models are great for most NLP tasks, yet both approaches have their limitations. Supervised models require labeled data, which is usually in…
Friday, September 27, 2024
3 min

Deduction Evaluation

logic
reasoning
deduction
goal create a deduction data-set for evaluating reasoning capabilities of a man and machine.
Thursday, September 26, 2024
2 min

Fine-tune llm for Style and Grammar advice.

NLP
LLMs are amazing - can I fine tune a state of the art LLM like Lama 3.1 with what I consider to be very high quality writing from my private library content to create a…
Wednesday, September 25, 2024
5 min

Is compositionality overrated? The view from language emergence

review
compositionality
neural networks
signaling systems
language evolution
complex signaling system
A review of Marco Baroni’s talk on the emergence of languages and the role of compositionality in language evolution.
Sunday, September 1, 2024
29 min

Six quick tips to improve modeling

The following tips are from (Gelman and Hill 2007) Data Analysis Using Regression and Multilevel/Hierarchical Models by Andrew Gelman and Jennifer Hill.
Monday, August 26, 2024
3 min

Stumpy

Times Series Analysis
Stumpy (Law 2019) is a powerful and scalable library for computing a matrix profile which can be used for a variety of time series data mining tasks.
Thursday, August 8, 2024
6 min

replay buffer questions

we should aim to keep full options traces in the buffer
Tuesday, July 2, 2024
3 min

two ideas on generalization

The first idea comes from looking at regression and hyperparameter optimization tasks
Monday, July 1, 2024
6 min

Mesa & RL

Ifs we can store state, action, reward trajectories (to a file) this would facilitate
Tuesday, June 25, 2024
3 min

zero inflated data

Zero inflated data is a type of data that has a large number of zero values.
Sunday, June 23, 2024
6 min

readings in rl

rl
reinforcement learning
papers
notes
reading
rl-papers
rl-algorithms
rl-resources
A list of RL-papers and resources that I have read or plan to read.
Tuesday, June 18, 2024
9 min

Hyperparameter Optimization

one the idea is for a set of Hyperparameters to find the best one.
Thursday, June 13, 2024
2 min

More Sugar please

sugarscape
multi-agent simulation
agent-based modeling
agent-based social simulation
multi-agent reinforcement learning
sequential social dilemmas
cooperation
Markov games
non-cooperative games
complex signaling system
In Sugar ad Astra I covered some research questions I had about Sugarscape. Today I’d like to mediate on some ideas I have for extending sugarscape to make it more of…
Tuesday, June 11, 2024
24 min

Risk-constrained Markov decision processes

paper review
paper review
risk-constrained MDPs
stochastic optimization
CVaR
decision-making under uncertainty
by Vivek Borkar and Rahul Jain
Tuesday, June 11, 2024
5 min

Evolutionary Games and Population Dynamics Summary

mathematics
evolutionary games
population dynamics
Lotka-Volterra
dynamical systems
logistic growth
predator-prey model
I’ve recently come across a book called “Evolutionary Games and Population Dynamics” by Josef Hofbauer and Karl Sigmund.
Sunday, May 12, 2024
3 min

Roth Erev learning in Lewis signaling games

signaling games
reinforcement learning
Lewis signaling games
language evolution
signaling systems
neural networks
emergent languages
deep learning
complex signaling system
I wish now to implement learning in the Lewis signaling game. In the book some reinforcement learning RL algorithms are presented in some detail and a few variations are…
Thursday, May 9, 2024
44 min

Signals Experiment

Leaning language games
some refactoring ideas:
Tuesday, May 7, 2024
16 min

ad hoc complex signaling systems

a review and proposal
signaling games
emergent languages
complex signaling system
A deep dive into the complex signaling systems
Sunday, May 5, 2024
4 min

Shannon Game

emergent complex communications protocols
signaling games
compositionality
communication protocols
emergent languages
complex signaling system
In this note I want to start to explore one of my notions of compositionality of Lewis games with another game. In my thinking currently consider at least three senses for…
Thursday, May 2, 2024
12 min

Urn models using Numpy

probability
urn models
emergent languages
“There is a tendency in our planning to confuse the unfamiliar with the improbable. The contingency we have not considered seriously looks strange; what looks strange is…
Thursday, May 2, 2024
19 min

RAD REPL

TODO: 1. [x] basic REPL 2. [x] command based class 3. [x] add task command 4. [x] list tasks command 5. [x] set current task command 6. [x] complete task command
Wednesday, May 1, 2024
5 min

Mesa Lessons

reinforcement learning
mesa
agent-based modeling
sugarscape
Implementing Sugarscape has some interesting lessons.
Sunday, March 31, 2024
23 min

Sugar Scapes

Agent movement rule M:
Sunday, March 31, 2024
3 min

OCR building blocks

code
buggy code
TODO
OCR
split into:
Thursday, March 28, 2024
3 min

Patric Winston

A definition by Patrick Henry Winston

For Artificial Intelligence
kb-ai
speaking
rhetoric
awsome-learning
ai
Rumpelstiltskin principle
Patrick Henry Winston provides a definition of AI. How he keeps expanding his definition as he goes along is thing of beauty. It expands organicaly to incorporate new ideas, accommodate example problems and aspects of their solutions. This is a powerful example of using inductive thinking to create definition using a philosophical approach.
Sunday, March 3, 2024
2 min

OCR - Brain Dump

linkage
brain dump
OCR
Working of OCR articles by Susmith Reddy
Sunday, February 25, 2024
2 min

Rhetoric NLP Tasks

rhetoric
nlp
ideas
I recently have been annotating speeches following up on the edx a course on Rhetoric.
Saturday, February 17, 2024
3 min

Lewis Game from a Bayesian Perspective

Some thoughts on the Lewis signaling game
signaling games
Lewis signaling games
emergent languages
complex signaling system
Some thoughts on the Lewis signaling game
Monday, February 12, 2024
8 min

mermaid logo

😁 Quarto 💖 Mermaid🧜 Mindmaps 🧠

Quarto at last supports Mindmap charts using Mermaid charts.
Monday, February 12, 2024
2 min

man standing beside pipes by Kaique Rocha

The Great Migration

From Blogger to Jekyl and finaly to Quarto.
quarto
blogging
code
some migration notes from Blooger to Jekyl to Quarto blog.
Tuesday, January 30, 2024
2 min

Post With Code

news
code
analysis
This is an obligatory post with executable code.
Sunday, January 28, 2024
4 min

Engineering Reinforcement Learning Algorithms

As I progressed though the RL specialization I came to realize that the research is mostly about coming up with a new algorithm that works better. This is tricky and so in…
Wednesday, January 10, 2024
3 min

SuperLearner

demos
code
r
SuperLearner is an ensambeleing library.
Wednesday, January 10, 2024
18 min

Understanding Emergent Languages

NLP
language evolution
emergent languages
complex signaling system
Okay after taking a break, today I’ve been rethinking Complex Lewis signaling systems and the equilibria. I slow make progress in this area by considering a number of…
Thursday, January 4, 2024
90 min

D3.js in in Quarto Observable

code
d3.js
observable.js
So I’ve migrated my sample to Quarto – which supports d3.js via Observable and without the need for whack hacks
Tuesday, January 2, 2024
4 min

AutoGluon Cheetsheets

Beacuase auto-ml is a Superpower
cheatsheets
code
data science
auto-ml
Autogluon is a auto-ml framework, here are three cheetsheet for accellerating data science workloads
Wednesday, December 20, 2023
1 min

Spark Tips

BigData
Spark
https://stackoverflow.com/questions/30245180/what-do-the-numbers-on-the-progress-bar-mean-in-spark-shell#:~:text=This%20progress%20indicator%20means%20that,number%20of%20task…
Thursday, June 1, 2023
1 min

Summary: Synthesis and Stabilization of Complex Behaviors through Online Trajectory Optimization

Reinforcement Learning
Model Based RL
Model Predictive Control
MPC
LQR
MuJoCo
iLQG
Cost Functions
Iterative LQG Method
Numerical Methods
Optimal Control
Trajectory Optimization
Complex Behaviors
Humanoid Robots
Physics Simulator
Real-Time Control
Robustness
Planning
Robtics
Coursera
This paper was referenced by Drew Bagnell in the Coursera RL specilization for using simple quadratic approximation to learn a model in a continous control setting. The paper presents a method for online trajectory optimization, particularly focusing on complex humanoid robots performing tasks such as getting up from an arbitrary pose and recovering from large disturbances using dexterous maneuvers.
Thursday, June 1, 2023
4 min

MCMC algorithms

The procedure MetropolisHastings takes as input : - the target distribution p(x), - the proposal distribution q(x,y), - the initial sample x_0, and - the total number of…
Saturday, April 22, 2023
4 min

Quarto loves pseudocode

\begin{algorithm} \caption{Quicksort} \begin{algorithmic} \Procedure{Quicksort}{$A, p, r$} \If{$p < r$} \State $q = $ \Call{Partition}{$A, p, r$} \State…
Tuesday, April 11, 2023
1 min

slide

Text2topic Leverage reviews data for multi-label topics classification in Booking.com

NLP.IL
Having millions of customer reviews, we would like to better understand them and leverage this data for different use cases. For example, finding popular activities per…
Tuesday, February 28, 2023
2 min

slide

Validating NLP data and models

NLP.IL
NLP data, and unstructured data in general, is very hard to validate. Validating NLP data is a real challenge, as actions such as statistical analysis and segmentation…
Tuesday, February 28, 2023
2 min

Transformations in Linguistic Representation

nlp
linguistics
In computational linguistics, using different representations can shed light on the structure of language. I’m considering how sentences can be depicted using parse trees or…
Wednesday, February 22, 2023
4 min

event generator

news
code
analysis
prompt engineering
fake data
Thursday, February 16, 2023
6 min

OLS regression From Scratch

data science
ml
algorithms
OLS regression is a method for estimating the parameters of a linear regression model. The goal is to find the line that best fits a set of data points. The line is…
Wednesday, February 1, 2023
2 min

entropy for uncertainty quantification

There is an e-commerce store. Every day it collects the cost, sales and shelf price for each product. Let’s say we also have to deduct a sales tax or value added tax say at…
Thursday, September 22, 2022
7 min

wikisym 2012 logo

Wikisym 2012

Conference Report
report
wikisym
conference
Due to a kind grant by the WikiMedia Foundation I was able to attend Wikisym 2012 in Linz Austria what follows is my report on the event.
Tuesday, July 26, 2022
8 min

Set Up M1 MacBooks for DS & ML

mac
Set Up M1 MacBooks for DS & ML
Thursday, May 5, 2022
1 min

command line

productivity
mac
command line cheea sheet macos + zsh + git
Thursday, May 5, 2022
21 min

Meme bank

memes a problem-solving approach
meme
TRIZ
tetrad
brainstorm
algorithm
A meme is an idea, behavior, style, or usage that spreads from person to person within a culture. A meme bank would be a zoo for cataloging and breeding memes.
Thursday, December 30, 2021
4 min

Getting more from your agency ?

digital marketing agencies.
marketing
digital marketing
agency
Getting more from your digital marketing agency, my five cents on picking your agency.
Monday, September 27, 2021
8 min

Attention for sensor fusion

attention
data science
marketing
sensor fusion
statistics
autoecoder
Attention for sensor fusion
Friday, September 24, 2021
5 min

Excel 2019 for Marketing Statistics in pandas

data science
statistics
marketing
Excel 2019 for Marketing Statistics in pandas
Friday, September 24, 2021
2 min

Language models and explainability

data science
statistics
marketing
NLP
Language models and explainability
Friday, September 24, 2021
17 min

Storytelling and other essentials

data science
statistics
marketing
war story
Storytelling and other essentials,
Thursday, September 2, 2021
4 min

Python Graphs

PPC
code
data science
digital marketing
quantitative marketing
intelligence
Python Graph Cookbook
Sunday, August 29, 2021
3 min

Stochastic Gradient Descent - The good parts

Stochastic Gradient Descent - The good parts
Sunday, August 29, 2021
14 min

WaveNet

paper review
deep learning
data science
NLP
The WaveNet paper is kind of old. Yet it seems to come up in various contexts. Some thoughts on this.
Sunday, August 29, 2021
4 min

What is in a citation?

Creating Citation Web Components
Sunday, August 29, 2021
4 min

Hackathon session link dumps & notes

modelling
chat bot
wikipedia
support
Wikipedia Hackathon notes
Friday, August 13, 2021
2 min

Inlining Citations for Wikipedia articles

modelling
chat bot
wikipedia
support
An algorithm for Inlining Citations for Wikipedia articles.
Friday, August 13, 2021
11 min

Transfer learning in NLP

modelling
chat bot
wikipedia
support
Transfer learning in NLP
Thursday, August 12, 2021
3 min

A type of Witness and an evolving Idiom

writing better code = writing more readable code.
Wednesday, July 14, 2021
2 min

json-ld

metadata format for linked data
information science
I’ve been excited about JSON-LD, when it came out as it offered a much cleaner way to do SEO. However It dawned on me later that it is also a geat format to worked with…
Thursday, July 1, 2021
4 min

TensorFlow probability

ML
AI
NLP
Bijectors
Auto Regressive Flows
In a recent google ai blog post an transformer based autoencoder is shown that can be used to learn and generate document layouts.
Tuesday, June 1, 2021
1 min

Ebook Hacks

hacks
ebooks
resolution
A number of djvu docs collected over a long time need to be convert them into pdf.
Saturday, May 29, 2021
2 min

Multilevel Models

NLP
notes
summarization task
lecture notes
bibliography
literature review
Different Multilevel Models Types
Sunday, May 16, 2021
9 min

Q&A and the Winograd schemas

idea
NLP
intelligence
resolution
The classical Q&A task is fairly easy to solve. But how well does the IR system understand/model the data. The challenge to test this aspect of the system is to provide test…
Tuesday, April 27, 2021
4 min

Automatic Summarization Task

NLP
notes
summarization task
lecture notes
bibliography
literature review
video
automatic extracting
automatic abstracting
sentence selection
document screening
sentence significance
relevance
content words
key words
pragmatic words
cue words
title words
sentence location
research methodology
parameterization
comparative evaluation
Concepts, slide commentaries and Lecture notes on Automatic text Summarization by Masa Nekic
Saturday, April 24, 2021
17 min

Bayesian agents

idea
game theory
bayesian games
sub-perfect bayesian equilibrium
Let’s try to define a KR framework for a Bayesian agent.
Wednesday, April 14, 2021
6 min

Modeling Events

modelling
data science
Modeling Events.
Friday, April 9, 2021
8 min

10 Tips To Improve Your Workflow

How to blog like a life-hacker.
Wednesday, April 7, 2021
3 min

Language Models Are Open Knowledge Graphs

paper review
paper
language models
deep learning
data mining
NLP
A review of the paper “Language Models are Open Knowledge Graphs” by Chenguang Wang, Xiao Liu, Dawn Song arXiv:2010.11967
Wednesday, April 7, 2021
7 min

Linkage 2021-04-07

links
Cleaning up my Tabs:
Wednesday, April 7, 2021
2 min

Jekyll take 3

Getting
blogging
ruby
jekyll
My attempts to get the jekyll version of this site to also build locally.
Sunday, April 4, 2021
3 min

MathJax 3 fix for Jekyll hosted on Github pages

blogging
jekyll
kramdown
mathjax
Issues and workarounds for MatchJax 3.0.
Sunday, April 4, 2021
2 min

Effective Approaches to Attention-based NMT

Paper review for the deeplearning.ai NLP specialization
nlp
coursera
notes
paper
attention
deep learning
literature review
Review of the paper on dot product attention for the deeplearning.ai NLP specialization.
Sunday, March 21, 2021
6 min

numpy melt down

python
macos
bugs
numpy melt down.
Sunday, November 29, 2020
1 min

Deep Learning Intuitions

intuition
data analysis
python
deep learning
Stacking n-layers RELUS in a feed forward neural network is functionally equivalent to a set of nested inequalities.
Sunday, October 25, 2020
2 min

brace expansion

bash
command line
linux
  • the bash shell supports brace expansion.
  • the idea is that the string before and after are concatenated with element in the braces
echo "you won "{two,three,four}"…
Friday, June 12, 2020
1 min

Pandas Productivity Challenge?

data-science
python
data-wrangling
Just a little rant on Pandas various contexts
Wednesday, March 4, 2020
7 min

How to avoid cross site scripting (XSS) errors with the Jupyter local runtime for Colab

data-science
ds-tips
Google-colab
colab
jupyter
python
R
tool-tip
data analysis
XSS
So the trick is
Thursday, February 20, 2020
1 min

Docker for data science

docker
conternerization
data analysis
Post description
Sunday, November 24, 2019
1 min

Exploding and vanishing nodes.

brain farts
One paradgm is that the network could be dynamic. For such a model we want to be able to add and remove nodes. This could be an issue for networks that are engineered to…
Wednesday, July 31, 2019
2 min

text annotation with BRAT

BRAT is a rapid annotation tool. Its old no long maintained - the original developers seem to have moved on. Requests for RTL support have been largely ignored. Some…
Tuesday, January 16, 2018
1 min

A/B testing cost and risks?

PPC,
data science,
digital marketing,
quantitative marketing,
CRO,
experimental design,
A/B testing
A/B testing cost and risks and some recommendation.
Sunday, July 30, 2017
12 min

Travel checklist

life hacks for travel
travel
checklist
    • Wednesday, December 14, 2016
    1 min

    HotJar Heat Map Analysis - Dr. David Darmanin

    All things data 2015
    Conference
    Analytics
    Heat Maps
    What are Heatmaps
    Wednesday, April 20, 2016
    2 min

    Using Competitive Analysis to Benchmark Your Marketing Efforts Ariel Rosenstein - Similar Web

    All things data 2015
    all things data
    conference
    analytics
    orgenizational behviour
    Mr Jerbi’s Background:       Come to web analytics from academia Industry and Management - Scheduling and QA.       Recalls that before it was bought by Google Urchin cost…
    Monday, April 20, 2015
    2 min

    Using Competitive Analysis to Benchmark Your Marketing Efforts - Ariel Rosenstein - Similar Web

    All things data 2015
    Marketing
    Analytics
    Competitive Analysis
    Ari is the Sr. Marketing Director at Similarweb
    Monday, April 20, 2015
    1 min

    Analytics Checklist

    Saturday, February 7, 2015
    2 min

    life hacks

    life
    hacks
    health
    productivity
    Health and supplements:
    Friday, June 7, 2013
    9 min

    Text Mining With Python

    a number of NLP tasks in Python
    python
    NLP
    text mining
    code
    processing unknown tokens
    Tuesday, November 29, 2011
    6 min

    Text Mining With R

    a number of NLP tasks in R
    R
    NLP
    text Mining
    code
    Computational Linguistics tasks:
    Tuesday, November 29, 2011
    3 min

    Tidy Text Mining With R

    an update on NLP with R
    R
    NLP
    Text Mining
    tidyverse
    code
    Computational Linguistics tasks:
    Tuesday, November 29, 2011
    9 min

    Photo by Pixabay

    Time management Tips

    We could all use a productivity boost
    time management
    productivity
    Effective time management is crucial for success in both personal and professional life. With the right approach, you can achieve more in less time while maintaining a healthy work-life balance
    Thursday, August 11, 2011
    3 min
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