Aggressive geometry – Temporal complexity of a quantified linear program without free variables with only existential quantifications

All known examples of lower double exponential bounds for real quantizer elimination without free variables (essentially a decision problem) involve polynomial inequalities with degree $> 1 $

Is there an example of double exponentiation with polyhedral inequalities where polyhedral inequalities relate to degree? $ 1 $ for the case of non-free variables?

We know $ exists x in mathbb R ^ n: Axis leq b $ is a standard linear program.

I mainly look at the following case of quantized linear program without any free variable with only existential quantifications.

Can we still solve programs like $$ exists x_1 in mathbb R ^ {n_1} points exists x_t in mathbb R ^ {n_t} $$$$ A_1 (x_1, x_2) ^ T leq b_1 coin dots coin A_ {t-1} (x_ {t-1}, x_t) ^ T leq b_ {t-1} $$
$$ exists x_1 in mathbb R ^ {n_1} points exists x_t in mathbb R ^ {n_t} $$$$ A_1 (x_1, x_2) ^ T leq b_1 corner A_2 (x_1, x_2, x_3) ^ T leq b_2 coin dots corner A_ {t-1} (x_1, points, x_ {t- 1}, x_t) ^ T leq b_ {t-1} $$
at the hour $ mathsf {poly} (t, sum_ {i = 1} ^ t (m_i + n_i)) $ or $ A_i $ are matrices in $ mathbb R ^ {m_i times n_i} $ and $ b_i $ are vectors in $ mathbb R ^ {m_i} $ by collapse quantifications into one big $ exists $ quantify and consider as a standard linear program and solve through standard linear programming techniques?

Or is it possible that there are scenarios in which the program would require time $$ big ( sum_ {i = 1} ^ t (m_i + n_i) big) ^ {2 ^ {O (t)}} mathsf {poly} (t, sum_ {i = 1} ^ t (m_i + n_i)) $$ or maybe as much as $$ 2 ^ {O big ( big ( sum_ {i = 1} ^ t (m_i + n_i) big) ^ t big)} mathsf {poly} (t, sum_ {i = 1} t (m_i + n_i))? $$

Related, connected, related: Elimination of the quantizer without free variables and without polyhedral inequalities

In this blog introductory article,, it is mentioned in the last line that "I do not know if a doubly exponential lower bound is known for the decision problem when there are no free variables".

I want to know if this comment applies to scenarios without alternation.

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The Pi network is a small group of people connected in a security circle stitched with other smaller security circles to create a "trust graph" that will help users know who to trust and deal with. The security circle is used to validate a person's identity in order to allow transparent and secure transactions in the Pi cryptocurrency market. This is to ensure that no fraudulent activity can take place in the network. .

The members of the core team

Nicolas Kokkalis – Chief Technology Officer Stanford Ph.D. and Instructor, Stanford First Class Decentralized Applications; combining distributed systems and human-machine interactions to bring cryptocurrency to ordinary people.

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· They will release an update during the fourth quarter of 2019 that will allow users to send their Pi coins to any other network user. This will be the beginning of seeing the true value of the piece. Personally, for me, I totally agree, especially if it was enough to download a single application.

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Much more than the network is moving to mass adoption

As they are currently in beta, you can extract Pi parts at higher rates because there are fewer users on the network. Like Bitcoin for example; Bitcoin mining 10 years ago, you could get some bitcoin every hour or so. Now you will get something around 0.000001 BTC per hour as there are now millions of miners (the extraction rate varies for everyone depending on their platform).

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Comment down if you joined the group so that I can add you to my circle of safety.

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Aggressive geometry – Pushing ahead of locally free sheaves and solving singularities

Let $ X $ to be a Noetherian, affine, isolated of dimension at least $ 2 $ and $ pi: widetilde {X} to X $ a resolution of singularities. Let $ mathcal {E} $ to be a locally free sheaf on $ widetilde {X} $ such as $ pi _ * mathcal {E} $ is free $ mathcal {O} _X $-module. is $ mathcal {E} $ necessarily trivial, that is to say a direct sum of copies of $ mathcal {O} _ { widetilde {X}} $?