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Anyone know a lender that is willing to do unsecured startup business loans to somebody with 720+ credit with no PG (personal guarantee)?

Meaning, the loan will be under the LLC/corporation and my personal assets won’t be liable.
SEMrush

I heard these loans exist but they’re difficult to find. If anybody knows such a lender, please chime in.

Much appreciated! Thanks.

 

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linear algebra – Can I guarantee that one index in a vector can be made larger than any other from a given set of vectors?

I have a set of vectors of length $N$ that I’m going to be adding or subtracting in various combinations. My goal is to prove that for each index in the resulting vector, there exists some combination of adding or subtracting the vectors that will make the value at that index have a value larger than any other index. I don’t necessarily need to know what the solution is, just that one exists.

e.g. if I have two vectors

$$v_1 = (1, 0)$$
$$v_2 = (0, 1)$$

then I know trivially that I can maximize the first position with $v_1-v_2$ and the second with $v_2 – v_1$.

One obviously necessary condition is that to have index $i$ large, there must be at least one vector where that index is non-zero. A reasonable first guess would be add up all the vectors with a positive number in that position and subtract the rest, but that doesn’t always work, e.g. if

$$v_1 = (2, 1)$$
$$v_2 = (1, 2)$$

then $v_1 + v_2$ has the two elements tied at $(3, 3)$. But a solution does exist: $v_1 – v_2 = (1, -1)$ has the first element the largest, and $v_2 – v_1 = (-1, 1)$ has the 2nd element largest.

I’ve taken enough math in my day that I recognize that “does such a solution exist” (for a given set of vectors) is probably answerable, but it’s been long enough that I don’t remember how to go about actually answer it. I imagine it’ll have something to do with determinants or eigenvalues or something. Any pointers on how to solve this, or under what conditions the answer to this question will be “yes”? I’m also interested if the question changes significantly if I allow some vectors to be left out of the sum. Thanks.

c ++ – uninitialized_move_if_noexcept with strong exception guarantee

I have implemented uninitialized_move_if_noexcept Algorithm is missing in the standard library and offers:

  • strong exception guarantee (If an exception is raised, the operation has no effect.) If the value type is nothrow move constructible or nothrow copy constructable

  • Basic / weak exception guarantee (If an exception is thrown, the operation leaves the objects in a valid state, that is, in a shifted state.) Otherwise, this is the best you can guarantee in the event of an unavoidable defect

Code:

#include 
#include 
#include 
#include 

template 
ForwardIt uninitialized_move_if_noexcept(InputIt first, InputIt last, ForwardIt d_first)
{
    using value_type = typename std::iterator_traits::value_type;

    ForwardIt current = d_first;

    try
    {
        while (first != last)
            std::construct_at(std::addressof(*(current++)), std::move_if_noexcept(*(first++)));

        return current;
    }
    catch (...)
    {
        // if std::move_if_noexcept performed a move
        if constexpr (std::is_nothrow_move_constructible_v || !std::is_copy_constructible_v)
        {
            while (d_first != current)
            {
                std::destroy_at(std::addressof(*first));
                std::construct_at(std::addressof(*(first++)), std::move(*(d_first++)));
            }
        }

        std::destroy(d_first, current);
        throw;
    }
}

Note that std::move_if_noexcept only makes a move if std::is_nothrow_move_constructible_v || !std::is_copy_constructible_v.

Optimizations for trivial types (like std::memcpy) are not listed here for the sake of clarity.

I'm interested in concerns or improvements you might make about exception security properties.

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postgresql – Does the order guarantee the chronological order by automatically incrementing the PK?

For example, let's say "increment automatically" means postgres SERIAL Pseudo-type, the short answer is "not always".

SERIAL Columns are implemented using standard SQL sequences that, when used by multiple concurrent sessions, may generate out-of-order values ​​if the CACHE The parameter is set to more than 1. The manual states the following:

[A] Although multiple sessions are guaranteed to assign different sequence values, the values ​​can be generated out of sequence if all sessions are considered. For example with a Cache Setting 10, session A may reserve values ​​1..10 and return nextval=1, then session B could reserve values ​​11..20 and return nextval=11 before session A was generated nextval=2. So with a Cache Hiring one it is safe to assume that nextval Values ​​are generated one after the other; with a Cache If the setting is greater than one, you should only assume that the nextval Values ​​are all different, not that they are generated purely sequentially.

leaving CACHE A value of 1 can affect performance in a high parallelism environment. So you have to choose what is more important to you.

In my opinion try to reuse SERIAL Keeping track of the order in which records are created is not a good idea as it may lead to a maintenance problem: the only promise of the sequence is to provide it something unique incremental value for everyone nextval If you rely on its behavior in certain circumstances, your application may behave unpredictably when the situation changes, e.g. The details of the sequence implementation will change in a future version of Postgres, or changes in your workload may require an increase in CACHE Frame. Using a suitable time stamp for the order is both more secure and semantically clear.

Maximum cut – separation guarantee in the Goemans Williamson algorithm

In the original paper in Goemans-Williamson paper for Max-Cut we have to sample a random vector r and
we spend
$$
S = {i: r ^ {T} x_ {i} geq 0 }
$$

Where $ x_ {i} $ are column vectors of a realizable solution of the SDP relaxation.

My question is whether we have guaranteed that there is one $ r $ so the output is max-cut?

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