Recent content by twoflower

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    Number of independent subcubes of a hypercube

    Number of "independent" subcubes of a hypercube Hello, I am trying to solve this problem: I have an n-dimensional hypercube and m of its vertices. Now I want to compute the maximum number of subcubes of the entire hypercube such that: - each subcube from the set may contain only those m...
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    Reproduction issue

    Why not? I can, indeed, end up with exponentially many organisms (exponentially many in n) - that was my concern. Is it really so obvious even if we take into account the limitation that each organism can reproduce only with polynomial (in n) amount of other organisms?
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    Reproduction issue

    I see. The universe (total population) is fixed and of the same size the whole time. It's only the subset which is growing.
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    Reproduction issue

    As I'm thinking about it again, now it seems clear to me that yes, we can end up with exponentially many organisms. I'm not sure what you mean for time to flow "independently of n", but we can imagine that time "happens" in discrete moments and only one thing can happen in each moment: two...
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    Reproduction issue

    Hello, let's have this scenario. We have a parameter n and a exponentially large (in n) universe of organisms. We are given a subset of this universe, which is only polynomially large. The only action which the organisms are able to do is that two compatible organisms join together and a new...
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    Is this sum exponential?

    Hello, I've been solving a problem which forces me to answer the question: "Is there a boolean function with exponential number (in variable count) of prime implicants of the length n - 1?" Anyway, during solving this problem I came to this point: Is the following sum exponential in 2n...
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    What is canonical and prime DNF?

    Hello, I'm little confused about canonical and prime DNF. I found on web that prime DNF is DNF consisting of exactly the set of the prime implicants. In school we've been told that canonical DNF is set of all prime implicants, so it gives me that prime DNF = canonical DNF. Then we...
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    Linear regression

    Homework Statement Consider model of linear regression: Y_i = \beta_0 + x_i \beta_1 + \epsilon_i i = 1, ..., 5, where \epsilon_i \sim \mathcal{N}(0, \sigma^2) are independent. Find expected value and variance of predicted values \widehat{Y}_i considering that observations are...
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    Confidence interval

    Let's say we know this: \sqrt{n}\left(\widehat{\theta} - \theta\right) \sim \mathcal{N}\left(0, \frac{1}{F(\theta)}\right) How do we get from this information to this expression of confidence interval for \theta? \left( \widehat{\theta} \pm...
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    Estimation of parameters using maximum likelihood method

    Homework Statement Let's have random value X defined by its density function: f(x; \beta) = \beta^2x \mbox{e}^{-\beta x} where \beta > 0 for x > 0 and f(x) = 0 otherwise. Expected value of X is EX = \frac{2}{\beta} and variance is \mbox{var } X = \frac{2}{\beta^2}. Next...
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    Recursively enumerable predicate

    Hi all, could someone please explain to me, why, having recursively enumerable predicate Q(x,y) which is not recursive, the function defined as f(x) \simeq \mu_{y} Q(x,y) doesn't define partially recursive function? Ok, here's the argument for it: the program will "try" if Q(x,y)...
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    Computing axis forces of a construction

    Thank you very much, Cyclovenom! However, I'm still not able to finish the exercise. Could you please advise me which of the bars are zero-force? (I mean they have a zero axis force). Thank you in advance.
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    Equivalent characterization of uniform convergence

    Hi all, I'm learning some calculus theory and I found one point I don't fully understand: \mbox{Let M} \subset \mathbb{R} \mbox{ be non-empty set and let } f, f_{n}, n \in \mathbb{N} \mbox{ be functions defined on M. Then the following is true:} f_n \rightrightarrows f \mbox{ on...
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    Computing axis forces of a construction

    Hi all, I'm trying to compute the axis forces in the construction I put to attachment. I already have computed the R forces, but I don't know where should I start computing the axis forces from, from which point. Could please someone give me some advice? Thank you very much, best regards.