Bibliography [AAG03] [AAGM03] [ACB17] [ADG+ 16] [AGG+ 21] [ALS10] Michael Abbott, Thorsten Altenkirch, and Neil Ghani. Categories of Containers. In Andrew D. Gordon, editor, Foundations of Software Science and Computation Structures, Lecture Notes in Computer Science, pages 23–38, Berlin, Heidelberg, 2003. Springer. Michael Abbott, Thorsten Altenkirch, Neil Ghani, and Conor McBride. Derivatives of Containers. In Gerhard Goos, Juris Hartmanis, Jan Van Leeuwen, and Martin Hofmann, editors, Typed Lambda Calculi and Applications, volume 2701, pages 16–30. Springer Berlin Heidelberg, Berlin, Heidelberg, 2003. Series Title: Lecture Notes in Computer Science. Martin Arjovsky, Soumith Chintala, and L ́eon Bottou. Wasserstein GAN, December 2017. arXiv:1701.07875 [cs, stat].
| #!/usr/bin/env bb | |
| (require '[babashka.process :refer [shell]]) | |
| (require '[cheshire.core :as json]) | |
| (require '[clojure.java.io :as io]) | |
| (require '[clojure.string :as str]) | |
| (require '[babashka.http-client :as client]) | |
| (import '(java.util Base64 UUID) | |
| '(java.nio.file Files Paths) | |
| '(java.text SimpleDateFormat) |
| using Catlab | |
| # Define the category of sets | |
| C = Category() | |
| # Define the presheaf to represent the data | |
| data = Presheaf(C) | |
| # Define the presheaf to represent the latent variables | |
| latent_variables = Presheaf(C) |
In the symphony of biological complexity, operadic compositions offer a maestro's insight into the cacophony of elements engaged in life's dance. An (\infty)-topos takes center stage, offering a canvas for the operadic structures that flourish within, each a mosaic piece of biotic ingenuity.
Consider the Gene Regulatory Networks, where genes become operations, orchestrated in an elegant harmony as operadic compositions enable abstraction from molecular chatter to the emergence of phenotypic anthems. Inputs, regal regulatory cues, translate into operatic expressions through this categorical fabric, demonstrating the conceptual alliance between biology and operadic perspectives [5].
[ \mathcal{O}(g_1, \ldots, g_n) \rightarrow G ]
Where (\mathcal{O}) allegorizes the operad of regulatory interplay, (g_i) the individual gene inputs, and (G) the genesis of expressive concord. In this diagrammatic spectacle, one denotes the transmutation of
| using CausalInference | |
| V = [:U, :T, :P, :O] | |
| g = digraph([1=>3, 2=>3, 3=>4, 2=>4, 1=>4]) | |
| # Can estimate total effect T=>O without observing U? | |
| u = 2 | |
| v = 4 | |
| ∅ = Set{Int}() | |
| observed = 2:4 | |
| collect(list_covariate_adjustment(g, u, v, ∅, observed)) |
3:30 nice to be up in San Francisco um so are we talking about um what I think is really exciting 3:37 development um in mathematics it's going to shape our future um which is really 3:42 the uh um the development over the last few years of lots of Technologies to have to to make uh machines and 3:49 computers um um help us do math um much more effectively um now this some to 3:57 some ense this is not new um we haveed used both machines and computers and I I use the terms slightly differently um
barton@grothendieck ~ % flox activate
flox [default] barton@grothendieck ~ % julia
_
_ _ _(_)_ | Documentation: https://docs.julialang.org
(_) | (_) (_) |
_ _ _| |_ __ _ | Type "?" for help, "]?" for Pkg help.
| | | | | | |/ _` | |
| | |_| | | | (_| | | Version 1.10.0 (2023-12-25)
_/ |\__'_|_|_|\__'_| | Official https://julialang.org/ release
| (define (filter? exp) | |
| (or (list-value? exp) | |
| (not? exp))) | |
| (define (conjoin conjuncts frame-stream) | |
| (conjoin-mix conjuncts '() frame-stream)) | |
| (define (conjoin-mix conjs delayed-conjs frame-stream) | |
| (if (null? conjs) | |
| (if (null? delayed-conjs) |
| remote: Enumerating objects: 921, done. | |
| remote: Counting objects: 100% (332/332), done. | |
| remote: Compressing objects: 100% (146/146), done. | |
| remote: Total 921 (delta 208), reused 230 (delta 180), pack-reused 589 | |
| Receiving objects: 100% (921/921), 5.98 MiB | 6.46 MiB/s, done. | |
| Resolving deltas: 100% (588/588), completed with 21 local objects. | |
| From github.com:ollama-webui/ollama-webui | |
| 76139fc..26f7a1c main -> origin/main | |
| 880f58e..02f364b dev -> origin/dev | |
| Updating 76139fc..26f7a1c |
In the quest to understand the profound implications of the trivial n-th cohomology group in computational complexity and cohomology, one must navigate the intricate topology of theoretical landscapes, beautified by the elegance of algebraic structures.
A cohomology group is generally constituted by these boundaries and cycles within an algebraic context. The triviality of an n-th cohomology group, specifically when the group is zero, indicates that every n-cycle is a boundary of some (n+1)-chain within the given complex. This embodies the notion that, computationally speaking, there are no holes or features of interest that survives through time or across a certain dimension that the group is indexing [1].
Significantly, in computational complexity, a trivial homology or cohomology group could greatly simplify the computational algorithms, such as those used in persistent homology. Such simplifications are due to the lack of intricate structure