Ecoer Logo
VOTING POWER100.00%
DOWNVOTE POWER100.00%
RESOURCE CREDITS100.00%
REPUTATION PROGRESS74.74%
Net Worth
7.716USD
STEEM
0.000STEEM
SBD
15.008SBD
Effective Power
6.864SP
├── Own SP
5.841SP
└── Incoming Deleg
+1.022SP

Detailed Balance

STEEM
balance
0.000STEEM
market_balance
0.000STEEM
savings_balance
0.000STEEM
reward_steem_balance
0.000STEEM
STEEM POWER
Own SP
5.841SP
Delegated Out
0.000SP
Delegation In
1.022SP
Effective Power
6.864SP
Reward SP (pending)
9.950SP
SBD
sbd_balance
3.755SBD
sbd_conversions
0.000SBD
sbd_market_balance
0.000SBD
savings_sbd_balance
0.000SBD
reward_sbd_balance
11.253SBD
{
  "balance": "0.000 STEEM",
  "savings_balance": "0.000 STEEM",
  "reward_steem_balance": "0.000 STEEM",
  "vesting_shares": "9512.263781 VESTS",
  "delegated_vesting_shares": "0.000000 VESTS",
  "received_vesting_shares": "1664.440956 VESTS",
  "sbd_balance": "3.755 SBD",
  "savings_sbd_balance": "0.000 SBD",
  "reward_sbd_balance": "11.253 SBD",
  "conversions": []
}

Account Info

nametrilo
id436965
rank178,301
reputation260842635885
created2017-11-10T14:39:27
recovery_accountsteem
proxyNone
post_count24
comment_count0
lifetime_vote_count0
witnesses_voted_for0
last_post2018-07-26T15:39:39
last_root_post2018-07-26T15:39:39
last_vote_time2017-11-24T11:27:45
proxied_vsf_votes0, 0, 0, 0
can_vote1
voting_power0
delayed_votes0
balance0.000 STEEM
savings_balance0.000 STEEM
sbd_balance3.755 SBD
savings_sbd_balance0.000 SBD
vesting_shares9512.263781 VESTS
delegated_vesting_shares0.000000 VESTS
received_vesting_shares1664.440956 VESTS
reward_vesting_balance20422.288325 VESTS
vesting_balance0.000 STEEM
vesting_withdraw_rate0.000000 VESTS
next_vesting_withdrawal1969-12-31T23:59:59
withdrawn0
to_withdraw0
withdraw_routes0
savings_withdraw_requests0
last_account_recovery1970-01-01T00:00:00
reset_accountnull
last_owner_update1970-01-01T00:00:00
last_account_update2017-11-12T17:15:45
minedNo
sbd_seconds0
sbd_last_interest_payment2017-11-22T23:17:15
savings_sbd_last_interest_payment1970-01-01T00:00:00
{
  "id": 436965,
  "name": "trilo",
  "owner": {
    "weight_threshold": 1,
    "account_auths": [],
    "key_auths": [
      [
        "STM7DDcChNA11Rs68bWVxeqMtJnumvntqQdZxATtxrSCbF1z35DVE",
        1
      ]
    ]
  },
  "active": {
    "weight_threshold": 1,
    "account_auths": [],
    "key_auths": [
      [
        "STM6CXaqoEkufS1bB8tBLGR54hqrKdGEVqRrshZhqaVqphJga7pRG",
        1
      ]
    ]
  },
  "posting": {
    "weight_threshold": 1,
    "account_auths": [],
    "key_auths": [
      [
        "STM6PnMMxtkcx9AccrAJ5QrHu16RjpNCePBbpoZZHQAkVaYfD3Byv",
        1
      ]
    ]
  },
  "memo_key": "STM5mnzvh6jUsmdbhpkdkNtZKZYSx1o6mKq5Jxrw1xA3pPfMjpxqp",
  "json_metadata": "{\"profile\":{\"cover_image\":\"https://img.esteem.ws/fhgrkw2nrp.jpg\",\"profile_image\":\"https://steemitimages.com/DQmY83uaAifd5KqpyW3m2rdk7rjsHmhdV8eWr7e3WrJmHrp/22709509_351533171961331_4012022817703854080_n.jpg\"}}",
  "posting_json_metadata": "{\"profile\":{\"cover_image\":\"https://img.esteem.ws/fhgrkw2nrp.jpg\",\"profile_image\":\"https://steemitimages.com/DQmY83uaAifd5KqpyW3m2rdk7rjsHmhdV8eWr7e3WrJmHrp/22709509_351533171961331_4012022817703854080_n.jpg\"}}",
  "proxy": "",
  "last_owner_update": "1970-01-01T00:00:00",
  "last_account_update": "2017-11-12T17:15:45",
  "created": "2017-11-10T14:39:27",
  "mined": false,
  "recovery_account": "steem",
  "last_account_recovery": "1970-01-01T00:00:00",
  "reset_account": "null",
  "comment_count": 0,
  "lifetime_vote_count": 0,
  "post_count": 24,
  "can_vote": true,
  "voting_manabar": {
    "current_mana": "11176704737",
    "last_update_time": 1752868293
  },
  "downvote_manabar": {
    "current_mana": 2794176184,
    "last_update_time": 1752868293
  },
  "voting_power": 0,
  "balance": "0.000 STEEM",
  "savings_balance": "0.000 STEEM",
  "sbd_balance": "3.755 SBD",
  "sbd_seconds": "0",
  "sbd_seconds_last_update": "2017-11-22T23:17:15",
  "sbd_last_interest_payment": "2017-11-22T23:17:15",
  "savings_sbd_balance": "0.000 SBD",
  "savings_sbd_seconds": "0",
  "savings_sbd_seconds_last_update": "1970-01-01T00:00:00",
  "savings_sbd_last_interest_payment": "1970-01-01T00:00:00",
  "savings_withdraw_requests": 0,
  "reward_sbd_balance": "11.253 SBD",
  "reward_steem_balance": "0.000 STEEM",
  "reward_vesting_balance": "20422.288325 VESTS",
  "reward_vesting_steem": "9.950 STEEM",
  "vesting_shares": "9512.263781 VESTS",
  "delegated_vesting_shares": "0.000000 VESTS",
  "received_vesting_shares": "1664.440956 VESTS",
  "vesting_withdraw_rate": "0.000000 VESTS",
  "next_vesting_withdrawal": "1969-12-31T23:59:59",
  "withdrawn": 0,
  "to_withdraw": 0,
  "withdraw_routes": 0,
  "curation_rewards": 9,
  "posting_rewards": 28142,
  "proxied_vsf_votes": [
    0,
    0,
    0,
    0
  ],
  "witnesses_voted_for": 0,
  "last_post": "2018-07-26T15:39:39",
  "last_root_post": "2018-07-26T15:39:39",
  "last_vote_time": "2017-11-24T11:27:45",
  "post_bandwidth": 0,
  "pending_claimed_accounts": 0,
  "vesting_balance": "0.000 STEEM",
  "reputation": "260842635885",
  "transfer_history": [],
  "market_history": [],
  "post_history": [],
  "vote_history": [],
  "other_history": [],
  "witness_votes": [],
  "tags_usage": [],
  "guest_bloggers": [],
  "rank": 178301
}

Withdraw Routes

IncomingOutgoing
Empty
Empty
{
  "incoming": [],
  "outgoing": []
}
From Date
To Date
steemdelegated 1.022 SP to @trilo
2025/07/18 19:51:33
delegatorsteem
delegateetrilo
vesting shares1664.440956 VESTS
Transaction InfoBlock #97436293/Trx 7d8f96579aae6a661d9a44c9f14c3ce40cc16eca
View Raw JSON Data
{
  "trx_id": "7d8f96579aae6a661d9a44c9f14c3ce40cc16eca",
  "block": 97436293,
  "trx_in_block": 3,
  "op_in_trx": 0,
  "virtual_op": 0,
  "timestamp": "2025-07-18T19:51:33",
  "op": [
    "delegate_vesting_shares",
    {
      "delegator": "steem",
      "delegatee": "trilo",
      "vesting_shares": "1664.440956 VESTS"
    }
  ]
}
steemdelegated 1.124 SP to @trilo
2022/02/25 09:37:33
delegatorsteem
delegateetrilo
vesting shares1830.890448 VESTS
Transaction InfoBlock #61923170/Trx d19c80f7c75dfeb508e902cd19a9303845a215fa
View Raw JSON Data
{
  "trx_id": "d19c80f7c75dfeb508e902cd19a9303845a215fa",
  "block": 61923170,
  "trx_in_block": 2,
  "op_in_trx": 0,
  "virtual_op": 0,
  "timestamp": "2022-02-25T09:37:33",
  "op": [
    "delegate_vesting_shares",
    {
      "delegator": "steem",
      "delegatee": "trilo",
      "vesting_shares": "1830.890448 VESTS"
    }
  ]
}
2019/11/10 15:37:30
parent authortrilo
parent permlinkduality
authorsteemitboard
permlinksteemitboard-notify-trilo-20191110t153729000z
title
bodyCongratulations @trilo! You received a personal award! <table><tr><td>https://steemitimages.com/70x70/http://steemitboard.com/@trilo/birthday2.png</td><td>Happy Birthday! - You are on the Steem blockchain for 2 years!</td></tr></table> <sub>_You can view [your badges on your Steem Board](https://steemitboard.com/@trilo) and compare to others on the [Steem Ranking](https://steemitboard.com/ranking/index.php?name=trilo)_</sub> **Do not miss the last post from @steemitboard:** <table><tr><td><a href="https://steemit.com/steemfest/@steemitboard/steemfest-meet-the-stemians-contest-the-mysterious-rule-revealed"><img src="https://steemitimages.com/64x128/https://cdn.steemitimages.com/DQmasWw4jQHwxng82DKxY6Q6tVg9mWcto4xcDURs8knFgCa/image.png"></a></td><td><a href="https://steemit.com/steemfest/@steemitboard/steemfest-meet-the-stemians-contest-the-mysterious-rule-revealed">SteemFest Meet The Stemians Contest - The mysterious rule revealed</a></td></tr></table> ###### [Vote for @Steemitboard as a witness](https://v2.steemconnect.com/sign/account-witness-vote?witness=steemitboard&approve=1) to get one more award and increased upvotes!
json metadata{"image":["https://steemitboard.com/img/notify.png"]}
Transaction InfoBlock #38056227/Trx 05d101f97096b12e7333e32a7de6432a524cc3a8
View Raw JSON Data
{
  "trx_id": "05d101f97096b12e7333e32a7de6432a524cc3a8",
  "block": 38056227,
  "trx_in_block": 7,
  "op_in_trx": 0,
  "virtual_op": 0,
  "timestamp": "2019-11-10T15:37:30",
  "op": [
    "comment",
    {
      "parent_author": "trilo",
      "parent_permlink": "duality",
      "author": "steemitboard",
      "permlink": "steemitboard-notify-trilo-20191110t153729000z",
      "title": "",
      "body": "Congratulations @trilo! You received a personal award!\n\n<table><tr><td>https://steemitimages.com/70x70/http://steemitboard.com/@trilo/birthday2.png</td><td>Happy Birthday! - You are on the Steem blockchain for 2 years!</td></tr></table>\n\n<sub>_You can view [your badges on your Steem Board](https://steemitboard.com/@trilo) and compare to others on the [Steem Ranking](https://steemitboard.com/ranking/index.php?name=trilo)_</sub>\n\n\n**Do not miss the last post from @steemitboard:**\n<table><tr><td><a href=\"https://steemit.com/steemfest/@steemitboard/steemfest-meet-the-stemians-contest-the-mysterious-rule-revealed\"><img src=\"https://steemitimages.com/64x128/https://cdn.steemitimages.com/DQmasWw4jQHwxng82DKxY6Q6tVg9mWcto4xcDURs8knFgCa/image.png\"></a></td><td><a href=\"https://steemit.com/steemfest/@steemitboard/steemfest-meet-the-stemians-contest-the-mysterious-rule-revealed\">SteemFest Meet The Stemians Contest - The mysterious rule revealed</a></td></tr></table>\n\n###### [Vote for @Steemitboard as a witness](https://v2.steemconnect.com/sign/account-witness-vote?witness=steemitboard&approve=1) to get one more award and increased upvotes!",
      "json_metadata": "{\"image\":[\"https://steemitboard.com/img/notify.png\"]}"
    }
  ]
}
steemdelegated 1.237 SP to @trilo
2018/11/26 19:50:45
delegatorsteem
delegateetrilo
vesting shares2013.984142 VESTS
Transaction InfoBlock #28046756/Trx 4ae0a7d55541e76a7cb3ec2ec6eb034525722a1d
View Raw JSON Data
{
  "trx_id": "4ae0a7d55541e76a7cb3ec2ec6eb034525722a1d",
  "block": 28046756,
  "trx_in_block": 9,
  "op_in_trx": 0,
  "virtual_op": 0,
  "timestamp": "2018-11-26T19:50:45",
  "op": [
    "delegate_vesting_shares",
    {
      "delegator": "steem",
      "delegatee": "trilo",
      "vesting_shares": "2013.984142 VESTS"
    }
  ]
}
2018/11/10 15:49:57
parent authortrilo
parent permlinkduality
authorsteemitboard
permlinksteemitboard-notify-trilo-20181110t154957000z
title
bodyCongratulations @trilo! You have received a personal award! [![](https://steemitimages.com/70x70/http://steemitboard.com/@trilo/birthday1.png)](http://steemitboard.com/@trilo) 1 Year on Steemit <sub>_Click on the badge to view your Board of Honor._</sub> **Do not miss the last post from @steemitboard:** <table><tr><td><a href="https://steemit.com/steemfest/@steemitboard/steemfest3-and-steemitboard-meet-the-steemians-contest"><img src="https://steemitimages.com/64x128/https://cdn.steemitimages.com/DQmeLukvNFRsa7RURqsFpiLGEZZD49MiU52JtWmjS5S2wtW/image.png"></a></td><td><a href="https://steemit.com/steemfest/@steemitboard/steemfest3-and-steemitboard-meet-the-steemians-contest">SteemFest3 and SteemitBoard - Meet the Steemians Contest</a></td></tr></table> > Support [SteemitBoard's project](https://steemit.com/@steemitboard)! **[Vote for its witness](https://v2.steemconnect.com/sign/account-witness-vote?witness=steemitboard&approve=1)** and **get one more award**!
json metadata{"image":["https://steemitboard.com/img/notify.png"]}
Transaction InfoBlock #27581417/Trx 8fccc35e7fb7bd9699e392953b127e5baa516204
View Raw JSON Data
{
  "trx_id": "8fccc35e7fb7bd9699e392953b127e5baa516204",
  "block": 27581417,
  "trx_in_block": 6,
  "op_in_trx": 0,
  "virtual_op": 0,
  "timestamp": "2018-11-10T15:49:57",
  "op": [
    "comment",
    {
      "parent_author": "trilo",
      "parent_permlink": "duality",
      "author": "steemitboard",
      "permlink": "steemitboard-notify-trilo-20181110t154957000z",
      "title": "",
      "body": "Congratulations @trilo! You have received a personal award!\n\n[![](https://steemitimages.com/70x70/http://steemitboard.com/@trilo/birthday1.png)](http://steemitboard.com/@trilo)  1 Year on Steemit\n<sub>_Click on the badge to view your Board of Honor._</sub>\n\n\n**Do not miss the last post from @steemitboard:**\n<table><tr><td><a href=\"https://steemit.com/steemfest/@steemitboard/steemfest3-and-steemitboard-meet-the-steemians-contest\"><img src=\"https://steemitimages.com/64x128/https://cdn.steemitimages.com/DQmeLukvNFRsa7RURqsFpiLGEZZD49MiU52JtWmjS5S2wtW/image.png\"></a></td><td><a href=\"https://steemit.com/steemfest/@steemitboard/steemfest3-and-steemitboard-meet-the-steemians-contest\">SteemFest3 and SteemitBoard - Meet the Steemians Contest</a></td></tr></table>\n\n> Support [SteemitBoard's project](https://steemit.com/@steemitboard)! **[Vote for its witness](https://v2.steemconnect.com/sign/account-witness-vote?witness=steemitboard&approve=1)** and **get one more award**!",
      "json_metadata": "{\"image\":[\"https://steemitboard.com/img/notify.png\"]}"
    }
  ]
}
steemdelegated 12.833 SP to @trilo
2018/07/26 16:48:39
delegatorsteem
delegateetrilo
vesting shares20897.347220 VESTS
Transaction InfoBlock #24518952/Trx 3da84798f0553fbe8351f9099ddfdbc9c55bf308
View Raw JSON Data
{
  "trx_id": "3da84798f0553fbe8351f9099ddfdbc9c55bf308",
  "block": 24518952,
  "trx_in_block": 1,
  "op_in_trx": 0,
  "virtual_op": 0,
  "timestamp": "2018-07-26T16:48:39",
  "op": [
    "delegate_vesting_shares",
    {
      "delegator": "steem",
      "delegatee": "trilo",
      "vesting_shares": "20897.347220 VESTS"
    }
  ]
}
trilopublished a new post: duality
2018/07/26 15:57:45
parent author
parent permlinkmath
authortrilo
permlinkduality
titleDuality
body@@ -2626,24 +2626,36 @@ standing of +what taking the transpos @@ -2668,16 +2668,22 @@ matrix +means and I tr @@ -3153,16 +3153,17 @@ ch cases +, I embod
json metadata{"tags":["math","steemstem","story","science","optimization"],"image":["https://cdn.steemitimages.com/DQmazJd56qTkL9413KPK6CWE2XKSxpa1bzjT7UjxgrrH34X/image.png"],"app":"steemit/0.1","format":"markdown"}
Transaction InfoBlock #24517936/Trx 7afde532ba186f7507064a0e73b5e868c0568708
View Raw JSON Data
{
  "trx_id": "7afde532ba186f7507064a0e73b5e868c0568708",
  "block": 24517936,
  "trx_in_block": 40,
  "op_in_trx": 0,
  "virtual_op": 0,
  "timestamp": "2018-07-26T15:57:45",
  "op": [
    "comment",
    {
      "parent_author": "",
      "parent_permlink": "math",
      "author": "trilo",
      "permlink": "duality",
      "title": "Duality",
      "body": "@@ -2626,24 +2626,36 @@\n standing of \n+what taking \n the transpos\n@@ -2668,16 +2668,22 @@\n  matrix \n+means \n and I tr\n@@ -3153,16 +3153,17 @@\n ch cases\n+,\n  I embod\n",
      "json_metadata": "{\"tags\":[\"math\",\"steemstem\",\"story\",\"science\",\"optimization\"],\"image\":[\"https://cdn.steemitimages.com/DQmazJd56qTkL9413KPK6CWE2XKSxpa1bzjT7UjxgrrH34X/image.png\"],\"app\":\"steemit/0.1\",\"format\":\"markdown\"}"
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trilopublished a new post: duality
2018/07/26 15:41:15
parent author
parent permlinkmath
authortrilo
permlinkduality
titleDuality
body<center>![](https://cdn.steemitimages.com/DQmazJd56qTkL9413KPK6CWE2XKSxpa1bzjT7UjxgrrH34X/image.png)</center> Moritz: Hey Max, I have a problem. Max: Yeah whats up? Moritz: I hate spending money on fruit, but I want to get my daily recommended amount of vitamins... Max (suddenly excited): Oh I can help you with that, thats just an optimization problem with constraints! Moritz (relieved): Great, I already know the prices of apples and bananas per kilo at the supermarket. Max: We'll call that 2D vector p for prices. Moritz: I also have a table that has two columns for apple and banana and three rows for vitamin A, B and C. It shows how much units of a particular vitamin is in a kilo of a certain fruit. Max: We'll call that 3x2 matrix M. Moritz: I also have a list of the recommended amount of each vitamin. Max: We'll call that 3D vector c for 'constraint'. Moritz: Great! So now I need to find out how many kilos of apples and how many kilos of bananas to buy. Max: We'll call the 2D vector that represents how much kilo of which fruit to buy x. In summary you are trying to minimize p_transpose * x while satisfying the constraint M * x >= c. Moritz: Ah that makes sense, so now all I need to do is solve these equations and... Max (interupting): I have another idea. I recently started a business selling vitamin supplements. I could sell some to you now. That way you don't have to go the supermarket. Moritz (surprised): Thats great! So how much are you selling vitamins A, B and C for per unit? I want to see if you can compete with the supermarket. Max (self aware and greedy): Look, I am no communist. I will determine the vitamin price vector y you mentioned by maximizing the amount of money I will make if I sell you the recommended amount of each vitamin. In other words I am trying to maximize c_transpose * y. Moritz (slightly offended): So you're just going to sell at the highest price possible? How do I know you're not ripping me off? Can you guarantee me that I will not pay you more than what I would have otherwise at the supermarket? Max (impatient): Let me finish! I guarantee that the price of all the vitamins in a fruit will never cost more than the fruit itself does at the supermarket. Moritz (taking a moment to understand what Max is saying): So, for example, if I buy all the vitamins that are in a kilo of apples from you as supplements... Max: ...then I guarantee that you won't be spending more for the supplements than you would for the apples. So all in all, I guarantee that A_transpose * y <= p. Moritz (biting his lip): While this gave me a newfound understanding of the transpose of a matrix and I trust you that you won't break your guarantees, I am still left wondering whether it is really guaranteed that I wont get a worse deal than at the store. *A theorem descends from heaven* Duality Theorem: You have summoned me! Max and Moritz in unison: To what do we owe the pleasure?!! Duality Theorem: From my heavenly vantage point I can see that Max's maximization problem of finding y is the dual problem of Moritz's minimization problem of finding x. In such cases I embody the proof that Max's price will always be equal or better than the best supermarket price Moritz can find! In your case it is exactly equal for there is a unique solution for x and a unique solution for y! Moritz: Thats pretty cool, my dog. Max: I might have to rethink my business model... *Everyone in the story disappears in a cloud of glitter as the author of this post becomes aware that they are procrastinating instead of studying for their exams.*
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Transaction InfoBlock #24517607/Trx 30dc1edbbe75e7b78e87fc5f572bf7342885e487
View Raw JSON Data
{
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  "timestamp": "2018-07-26T15:41:15",
  "op": [
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    {
      "parent_author": "",
      "parent_permlink": "math",
      "author": "trilo",
      "permlink": "duality",
      "title": "Duality",
      "body": "<center>![](https://cdn.steemitimages.com/DQmazJd56qTkL9413KPK6CWE2XKSxpa1bzjT7UjxgrrH34X/image.png)</center>\n\nMoritz: Hey Max, I have a problem.\n\nMax: Yeah whats up?\n\nMoritz: I hate spending money on fruit, but I want to get my daily recommended amount of vitamins...\n\nMax (suddenly excited): Oh I can help you with that, thats just an optimization problem with constraints!\n\nMoritz (relieved): Great, I already know the prices of apples and bananas per kilo at the supermarket.\n\nMax: We'll call that 2D vector p for prices.\n\nMoritz: I also have a table that has two columns for apple and banana and three rows for vitamin A, B and C. It shows how much units of a particular vitamin is in a kilo of a certain fruit.\n\nMax:  We'll call that 3x2 matrix M.\n\nMoritz: I also have a list of the recommended amount of each vitamin.\n\nMax: We'll call that 3D vector c for 'constraint'.\n\nMoritz: Great! So now I need to find out how many kilos of apples and how many kilos of bananas to buy.\n\nMax: We'll call the 2D vector that represents how much kilo of which fruit to buy x. In summary you are trying to minimize p_transpose * x while satisfying the constraint M * x  >= c.\n\nMoritz: Ah that makes sense, so now all I need to do is solve these equations and...\n\nMax (interupting): I have another idea. I recently started a business selling vitamin supplements. I could sell some to you now. That way you don't have to go the supermarket.\n\nMoritz (surprised): Thats great! So how much are you selling vitamins A, B and C for per unit? I want to see if you can compete with the supermarket.\n\nMax (self aware and greedy): Look, I am no communist. I will determine the vitamin price vector y you mentioned by maximizing the amount of money I will make if I sell you the recommended amount of each vitamin. In other words I am trying to maximize c_transpose * y.\n\nMoritz (slightly offended): So you're just going to sell at the highest price possible? How do I know you're not ripping me off? Can you guarantee me that I will not pay you more than what I would have otherwise at the supermarket?\n\nMax (impatient): Let me finish! I guarantee that the price of all the vitamins in a fruit will never cost more than the fruit itself does at the supermarket.\n\nMoritz (taking a moment to understand what Max is saying): So, for example, if I buy all the vitamins that are in a kilo of apples from you as supplements...\n\nMax: ...then I guarantee that you won't be spending more for the supplements than you would for the apples. So all in all, I guarantee that A_transpose * y <= p.\n\nMoritz (biting his lip): While this gave me a newfound understanding of the transpose of a matrix and I trust you that you won't break your guarantees, I am still left wondering whether it is really guaranteed that I wont get a worse deal than at the store.\n\n*A theorem descends from heaven*\n\nDuality Theorem: You have summoned me!\n\nMax and Moritz in unison: To what do we owe the pleasure?!!\n\nDuality Theorem: From my heavenly vantage point I can see that Max's maximization problem of finding y is the dual problem of Moritz's minimization problem of finding x. In such cases I embody the proof that Max's price will always be equal or better than the best supermarket price Moritz can find! In your case it is exactly equal for there is a unique solution for x and a unique solution for y!\n\nMoritz: Thats pretty cool, my dog.\n\nMax: I might have to rethink my business model...\n\n*Everyone in the story disappears in a cloud of glitter as the author of this post becomes aware that they are procrastinating instead of studying for their exams.*",
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hackerzizonupvoted (1.00%) @trilo / duality
2018/07/26 15:40:18
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trilopublished a new post: duality
2018/07/26 15:39:39
parent author
parent permlinkmath
authortrilo
permlinkduality
titleDuality
body<center>![](https://cdn.steemitimages.com/DQmazJd56qTkL9413KPK6CWE2XKSxpa1bzjT7UjxgrrH34X/image.png)</center> Moritz: Hey Max, I have a problem. Max: Yeah whats up? Moritz: I hate spending money on fruit, but I want to get my daily recommended amount of vitamins... Max (suddenly excited): Oh I can help you with that, thats just an optimization problem with constraints! Moritz (relieved): Great, I already know the prices of apples and bananas per kilo at the supermarket. Max: We'll call that 2D vector p for prices. Moritz: I also have a table that has two columns for apple and banana and three rows for vitamin A, B and C. It shows how much units of a particular vitamin is in a kilo of a certain fruit. Max: We'll call that 3x2 matrix M. Moritz: I also have a list of the recommended amount of each vitamin. Max: We'll call that 3D vector c for 'constraint'. Moritz: Great! So now I need to find out how many kilos of apples and how many kilos of bananas to buy. Max: We'll call the 2D vector that represents how much kilo of which fruit to buy x. In summary you are trying to minimize p_transpose * x while satisfying the constraint M * x >= c. Moritz: Ah that makes sense, so now all I need to do is solve these equations and... Max (interupting): I have another idea. I recently started a business selling vitamin supplements. I could sell some to you now. That way you don't have to go the supermarket. Moritz (surprised): Thats great! So how much are you selling vitamins A, B and C for per unit? I want to see if you can compete with the supermarket. Max (self aware and greedy): Look, I am no communist. I will determine the vitamin price vector y you mentioned by maximizing the amount of money I will make if I sell you the recommended amount of each vitamin. In other words I am trying to maximize c_transpose * y. Moritz (slightly offended): So you're just going to sell at the highest price possible? How do I know you're not ripping me off? Can you guarantee me that I will not pay you more than what I would have otherwise at the supermarket? Max (impatient): Let me finish! I guarantee that the price of all the vitamins in a fruit will never cost more than the fruit itself does at the supermarket. Moritz (taking a moment to understand what Max is saying): So, for example, if I buy all the vitamins that are in a kilo of apples from you as supplements... Max: ...then I guarantee that you won't be spending more for the supplements than you would for the apples. So all in all, I guarantee that A_transpose * y <= p. Moritz (biting his lip): While this gave me a newfound understanding of the transpose of a matrix and I trust you that you won't break your guarantees, I am still left wondering whether it is really guaranteed that I wont get a worse deal than at the store. *A theorem descends from heaven* Duality Theorem: You have summoned me! Max and Moritz in unison: To what do we owe the pleasure?!! Duality Theorem: From my heavenly vantage point I can see that Max's maximization problem of finding y is the dual problem of Moritz's minimization problem of finding x. In such cases I embody the proof that Max's price will always be equal or better than the best supermarket price Moritz can find! In your case it is exactly equal for there is a unique solution for x and a unique solution for y! Moritz: Thats pretty cool, my dog. Max: I might have to rethink my business model... *Everyone in the story disappears in a cloud of glitter as the author of this post becomes aware that they are procrastinating instead of studying for their exams.*
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2017/12/31 08:16:03
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triloreceived 11.253 SBD, 12.541 SP author reward for @trilo / bayesian-inference-for-people-with-existential-angst
2017/11/29 21:17:45
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2017/11/29 20:49:06
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2017/11/29 20:42:57
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2017/11/26 01:36:03
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2017/11/25 23:04:51
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2017/11/25 23:04:33
parent authortrilo
parent permlinkre-terenceplizga-re-trilo-encoding-model-basics-1-20171115t123546830z
authorterenceplizga
permlinkre-trilo-re-terenceplizga-re-trilo-encoding-model-basics-1-20171125t230408136z
title
bodyThanks. I hope some of it was beneficial. The devil is usually in the details on projects like this, so the sooner you can confront potential traps, the better. Re: matrices versus vectors: I tend to use the term "matrix" more since I always keep the numbers in that form until a matrix multiplication operation is required, then I unroll and roll the matrix as needed to use the optimized multiplication algorithm. Re: colors: If the inputs to the CNN are photos of real world objects, I would go with the multi-channel approach, because it's the closest thing to be inspired from biology. We have separate cones in the eyes for reds, greens, and blues, while other living organisms have even more diversity, adding cones from UV light and polarized light (useful for seeing underwater). If the retinal neural cells combine the inputs from the different cones, that's one thing, but I don't think they do. That said, I think the situation changes if the inputs to the CNN are fMRI images. Don't they basically contain false colors to indicate some level of intensity? If that's the case, I would expect grayscale encoding to work. Re: temporal characteristic of fMRI data: I was just going by personal experience. I underwent a brain MRI scan once, and it took 10 minutes. But the stats on the Wikipedia page you cited doesn't give me much confidence. I suspect that current techniques are not capturing a large amount of neural activations. Re: filtering out neural activations in the fMRI image that represent undesired sensory inputs: I understand your response, but just be aware that this might be a matter of relevance, not noise. If the noise follows a particular pattern, the CNN may wrongly incorporate that pattern into its predictions. Think of the old experiment that classified tanks from cars, and failed, because all the photos of cars were taken on sunny days, and all the photos of tanks were taken on cloudy days. The CNN in that experiment started focusing on the sky color as a feature, rather than treating it as irrelevant data. It wasn't noise from the classic sense (from information theory and communication channels), because it was deterministic and not random (although that was an unfortunate coincidence). From another perspective, this problem seems a lot like an NLP experiment that attempts to separate simultaneous conversations at a party where a number of microphones scattered among the crowd are recording voices. Incidentally, a Kaggle competition from a while ago used brain fMRI data. It might be useful to track down the winner of that competition and ask about the approach he or she took.
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      "body": "Thanks.  I hope some of it was beneficial.  The devil is usually in the details on projects like this, so the sooner you can confront potential traps, the better.  \n\nRe: matrices versus vectors:  I tend to use the term \"matrix\" more since I always keep the numbers in that form until a matrix multiplication operation is required, then I unroll and roll the matrix as needed to use the optimized multiplication algorithm.  \n\nRe: colors:  If the inputs to the CNN are photos of real world objects, I would go with the multi-channel approach, because it's the closest thing to be inspired from biology.  We have separate cones in the eyes for reds, greens, and blues, while other living organisms have even more diversity, adding cones from UV light and polarized light (useful for seeing underwater).  If the retinal neural cells combine the inputs from the different cones, that's one thing, but I don't think they do.  That said, I think the situation changes if the inputs to the CNN are fMRI images.  Don't they basically contain false colors to indicate some level of intensity?  If that's the case, I would expect grayscale encoding  to work.\n\nRe: temporal characteristic of fMRI data:  I was just going by personal experience.  I underwent a brain MRI scan once, and it took 10 minutes.  But the stats on the Wikipedia page you cited doesn't give me much confidence.  I suspect that current techniques are not capturing a large amount of neural activations. \n\nRe: filtering out neural activations in the fMRI image that represent undesired sensory inputs:  I understand your response, but just be aware that this might be a matter of relevance, not noise.  If the noise follows a particular pattern, the CNN may wrongly incorporate that pattern into its predictions.  Think of the old experiment that classified tanks from cars, and failed, because all the photos of cars were taken on sunny days, and all the photos of tanks were taken on cloudy days.  The CNN in that experiment started focusing on the sky color as a feature, rather than treating it as irrelevant data.  It wasn't noise from the classic sense (from information theory and communication channels), because it was deterministic and not random (although that was an unfortunate coincidence).  From another perspective, this problem seems a lot like an NLP experiment that attempts to separate simultaneous conversations at a party where a number of microphones scattered among the crowd are recording voices.  \n\nIncidentally, a Kaggle competition from a while ago used brain fMRI data.  It might be useful to track down the winner of that competition and ask about the approach he or she took.",
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2017/11/24 16:43:39
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2017/11/24 11:27:45
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      "profile_image": "https://steemitimages.com/DQmY83uaAifd5KqpyW3m2rdk7rjsHmhdV8eWr7e3WrJmHrp/22709509_351533171961331_4012022817703854080_n.jpg"
    }
  }
}

Auth Keys

Owner
Single Signature
Public Keys
STM7DDcChNA11Rs68bWVxeqMtJnumvntqQdZxATtxrSCbF1z35DVE1/1
Active
Single Signature
Public Keys
STM6CXaqoEkufS1bB8tBLGR54hqrKdGEVqRrshZhqaVqphJga7pRG1/1
Posting
Single Signature
Public Keys
STM6PnMMxtkcx9AccrAJ5QrHu16RjpNCePBbpoZZHQAkVaYfD3Byv1/1
Memo
STM5mnzvh6jUsmdbhpkdkNtZKZYSx1o6mKq5Jxrw1xA3pPfMjpxqp
{
  "owner": {
    "weight_threshold": 1,
    "account_auths": [],
    "key_auths": [
      [
        "STM7DDcChNA11Rs68bWVxeqMtJnumvntqQdZxATtxrSCbF1z35DVE",
        1
      ]
    ]
  },
  "active": {
    "weight_threshold": 1,
    "account_auths": [],
    "key_auths": [
      [
        "STM6CXaqoEkufS1bB8tBLGR54hqrKdGEVqRrshZhqaVqphJga7pRG",
        1
      ]
    ]
  },
  "posting": {
    "weight_threshold": 1,
    "account_auths": [],
    "key_auths": [
      [
        "STM6PnMMxtkcx9AccrAJ5QrHu16RjpNCePBbpoZZHQAkVaYfD3Byv",
        1
      ]
    ]
  },
  "memo": "STM5mnzvh6jUsmdbhpkdkNtZKZYSx1o6mKq5Jxrw1xA3pPfMjpxqp"
}

Witness Votes

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No active witness votes.
[]