Why does convexity/concavity in mathematics seem to contradict the dictionary definition?

In the usual mathematical definition of convexity, a function is #convex when it forms a “trough”, i.e. it curves downward, seen from above. I have always pictured it like that - seen from above, so it curves “inward”.

However, the dictionary definition says it means: “curved outwards, like the surface of an eye” [Cambridge Dictionary]. This also seems to be the interpretation for optical lenses.

'Gradient-free optimization of highly smooth functions: improved analysis and a new algorithm', by Arya Akhavan, Evgenii Chzhen, Massimiliano Pontil, Alexandre B. Tsybakov.

http://jmlr.org/papers/v25/23-0733.html

#gradient #convex #optimality

#Software #Alternatives #Quote

"...for every paid #SaaS, there is a #free #opensource #selfhosted #alternative:

#Zoom -> #Jitsi
#Notion -> #Appflowy
#Jira -> #Plane
#Airtable -> #NocoDB
#Vercel -> #Coolify
#Heroku -> #Dokku
#Firebase -> #Pocketbase / #Appwrite / #Convex / #Supabase
#Shopify -> #Prestashop
#GitHub -> #GitLab
#Slack -> #Mattermost
#Salesforce #CRM -> #ERPNext
#Dropbox -> #NextCloud
#Mailchimp -> #Mautic
#Trello -> #Wekan
#Docusign -> #Docuseal
#Calendly -> #Cal dot com
#Datadog -> #Prometheus
#Google #Analytics -> #Matomo
#Microsoft #Office365 -> #LibreOffice
#Asana -> #OpenProject

what else?

Reposted with hashtags from #Fireship #Quotes:
https://bird.makeup/users/fireship_dev/statuses/1828485695029260356

What do cool kids use for a serverless back end for their web apps? I was looking at #convex

'Fixed points of nonnegative neural networks', by Tomasz J. Piotrowski, Renato L. G. Cavalcante, Mateusz Gabor.

http://jmlr.org/papers/v25/23-0167.html

#nonnegative #nonlinear #convex

'Faster Rates of Differentially Private Stochastic Convex Optimization', by Jinyan Su, Lijie Hu, Di Wang.

http://jmlr.org/papers/v25/22-0079.html

#stochastic #optimal #convex

'Accelerated Primal-Dual Mirror Dynamics for Centralized and Distributed Constrained Convex Optimization Problems', by You Zhao, Xiaofeng Liao, Xing He, Mingliang Zhou, Chaojie Li.

http://jmlr.org/papers/v24/22-1069.html

#convex #optimization #mirror

'The Geometry and Calculus of Losses', by Robert C. Williamson, Zac Cranko.

http://jmlr.org/papers/v24/22-0987.html

#classification #convex #losses

'Multi-Consensus Decentralized Accelerated Gradient Descent', by Haishan Ye, Luo Luo, Ziang Zhou, Tong Zhang.

http://jmlr.org/papers/v24/22-1210.html

#convex #convexity #optimization

'Fast Objective & Duality Gap Convergence for Non-Convex Strongly-Concave Min-Max Problems with PL Condition', by Zhishuai Guo, Yan Yan, Zhuoning Yuan, Tianbao Yang.

http://jmlr.org/papers/v24/21-1471.html

#minimization #optimization #convex

#Anonymous leaked 128GB of data stolen from Russian ISP #Convex revealing #FSB's warrantless #surveillance
https://securityaffairs.com/141888/hacktivism/anonymous-fsb-surveillance.html
#securityaffairs #hacking #Russia

#Anonymous Hacktivisten haben 128 Gigabyte Daten von #Convex, dem führenden russischen Internetanbieter, veröffentlicht. Aus denen soll hervorgehen, wie umfangreich der #Kreml seine Bürger landesweit illegal überwacht.
#Russland #OpRussia
https://www.hackread.com/anonymous-data-leak-russia-isp-convex/

#Anonymous Leaks 128 GB of Data from #Russian ISP #Convex
https://www.hackread.com/anonymous-data-leak-russia-isp-convex/

RELEASE: 120 gigabytes from the Russian internet provider #Convex, revealing pervasive Russian surveillance of internet and phone activities, including the previously unknown Green Atom #surveillance program.
https://ddosecrets.com/wiki/Convex

In 2015, the European Court of Human Rights warned in Zakharov v. Russia that the legislation underpinning #Russia's System for Operative Investigative Activities surveillance system did "not provide for adequate and effective guarantees against arbitrariness and the risk of abuse which is inherent in any system of secret surveillance" and that the requirements for legal authorization could be circumvented. In 2016, the Yarovaya Law was passed and went into effect in 2018, requiring that all communications information be provided to authorities without a court order.

According to the hackers, the Green Atom data confirms the extent to which these legal structures are abused. They say the internet provider captured and mirrored virtually all data from every switch in the largest regions of Russia, which is then passed on to Moscow for use by the security services.

Data: https://ddosecrets.com/wiki/Convex

Help keep DDoSecrets operating in 2023 with a $15 donation: https://DDoSecrets.Charity

'Online Mirror Descent and Dual Averaging: Keeping Pace in the Dynamic Case', by Huang Fang, Nicholas J. A. Harvey, Victor S. Portella, Michael P. Friedlander.

http://jmlr.org/papers/v23/21-1027.html

#optimization #convex #averaging

Happy Sunday everyone!

Todays #fungifind 

The stages of a Shaggy Parasol! (Chlorophyllum rhacodes)

A Shaggy Parasol is a #large, stocky mushroom with a #convex cap when mature. The cap’s surface has raised #brown scales, giving it a #shaggy look, further enhanced by the shaggy edge to the #rim.

The shaggy parasol’s habit of #growing in rings, known as #fairy rings, has long been part of European #folklore. Some believe the #rings symbolised a place where #fairies, #pixies or #elves danced in the woods. Others believe that they were a #portal between the fairy world and the #human world!

On a side note, though #edible when cooked for some, I wouldn’t be #foraging this one for dinner because it can cause #severe gastric upset in 1 in 25 people!

#fungioftheday #shaggyparasol #toadstool #fungi #mushroom #nature #tinderfungus #mastodonmushrooms #mastodon #mastoart #mycodon #bracket #mosstodon #mycology #fungiverse #fungus #mushroomsofmastodon #nature
#fungifacts #mushrooms #plants #fungikingdom #mastodonmushroom