Résultats de recherche pour « Assembly Theory »

The functional Schrodinger picture formulation of quantum field theory and the variational Gaussian approximation method based on the formulation are briefly reviewed. After presenting recent attempts to improve the variational approximation, we introduce a new systematic method based on the background field method, which enables one to compute the order-by-order correction terms to the Gaussian approximation of the effective action.

Assembly theory measures a string by the shortest history that builds it. We sharpen this picture in two directions. First, we attach a discrete Dirichlet energy to an assembly space and show that it splits into the size of the space and a secondary energy charging each step vertex the square of its secondary (pathway depth) increment. The assembly index does not imply minimum energy, and the assembly depth and the energy are independent complexity measures. Second, we ask how an ensemble T of strings co-assembles within a single space. Defining step strings within an assembly space solely by their formation histories yields three joint assembly spaces: the collectively (\( \omega_T \)), multiplicity (\( \mu_T \)), and singly (\( \pi_T \)) optimal ones, where the latter need not exist for certain ensembles and \( |\omega_T| \le |\mu_T| \le |\pi_T| \). All three sizes can differ, and multiplicity can lower the singly optimal size only for ensembles with \( |\pi_T| - |\omega_T| \ge 2 \). Collective optimization is NP-complete, while singly and multiplicity optimizations are NP-hard and lie a priori in the second level of the polynomial hierarchy.

The Jupiter-Saturn 2:5 near-commensurability is analyzed in a fully analytic Hamiltonian planetary theory. Computations for the Sun-Jupiter-Saturn system, extending to the third order of the masses and to the 8th degree in the eccentricities and inclinations, reveal an unexpectedly sensitive dependence of the solution on initial data and its likely nonconvergence. The source of the sensitivity and apparent lack of convergence is this near-commensurability, the so-called great inequality. This indicates that simple averaging, still common in current semi-analytic planetary theories, may not be an adequate technique to obtain information on the long-term dynamics of the Solar System. Preliminary results suggest that these difficulties can be overcome by using resonant normal forms.

Assembly theory measures a string by the shortest history that builds it. We sharpen this picture in two directions. First, we attach a discrete Dirichlet energy to an assembly space and show that it splits into the size of the space and a secondary energy charging each step vertex the square of its secondary (pathway depth) increment. The assembly index does not imply minimum energy, and the assembly depth and the energy are independent complexity measures. Second, we ask how an ensemble T of strings co-assembles within a single space. Individuating step vertices by their formation histories rather than by the strings they carry yields three joint assembly spaces: the collectively (\( \omega_T \)), multiplicity (\( \mu_T \)), and singly (\( \pi_T \)) optimal ones, where the latter need not exist for certain ensembles and \( |\omega_T| \le |\mu_T| \le |\pi_T| \). All three sizes can differ, and multiplicity can lower the singly optimal size only for ensembles with \( |\pi_T| - |\omega_T| \ge 2 \). Collective optimization is NP-complete, while singly and multiplicity optimizations are NP-hard and lie a priori in the second level of the polynomial hierarchy.

Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number, where the assembly index is the minimum number of joining operations necessary to construct an object from basic parts, and the copy number is how many instances of the given object(s) are observed. Together these define a quantity, called Assembly, which captures the amount of causation required to produce objects in abundance in an observed sample. This contrasts with the random generation of objects. Herein we describe how AT's focus on selection as the mechanism for generating complexity offers a distinct approach, and answers different questions, than computational complexity theory with its focus on minimum descriptions via compressibility. To explore formal differences between the two approaches, we show several simple and explicit mathematical examples demonstrating that the assembly index, itself only one piece of the theoretical framework of AT, is formally not equivalent to other commonly used complexity measures from computer science and information theory including Shannon entropy, Huffman encoding, and Lempel-Ziv-Welch compression. We also include proofs that assembly index is not in the same computational complexity class as these compression algorithms and discuss fundamental differences in the ontological basis of AT, and assembly index as a physical observable, which distinguish it from theoretical approaches to formalizing life that are unmoored from measurement.

Assembly theory measures a string by the shortest history that builds it. We sharpen this picture in two directions. First, we attach a discrete Dirichlet energy to an assembly space and show that it splits into the size of the space and a secondary energy, charging each step vertex the square of its secondary (pathway depth) increment. The assembly index does not imply minimum energy, and the assembly depth and the energy are independent complexity measures. Second, we ask how an ensemble T of strings co-assembles within a single space. Individuating step vertices by their formation histories rather than by the strings they carry yields three joint assembly spaces: the collectively (ωT), multiplicity (μT), and singly (πT) optimal ones, where the latter need not exist for certain ensembles and ∣ωT∣ ≤ ∣μT∣ ≤ ∣πT∣. All three sizes can differ, and multiplicity can lower the singly optimal size only for ensembles with ∣πT∣ − ∣ωT∣ ≥ 2. Collective optimization is NP-complete, while singly and multiplicity optimizations are NP-hard and lie in the second level of the polynomial hierarchy.

We develop equilibrium and kinetic theories that describe the assembly of viral capsid proteins on a charged central core, as seen in recent experiments in which brome mosaic virus (BMV) capsids assemble around nanoparticles functionalized with polyelectrolyte. We model interactions between capsid proteins and nanoparticle surfaces as the interaction of polyelectrolyte brushes with opposite charge, using the nonlinear Poisson Boltzmann equation. The models predict that there is a threshold density of functionalized charge, above which capsids efficiently assemble around nanoparticles, and that light scatter intensity increases rapidly at early times, without the lag phase characteristic of empty capsid assembly. These predictions are consistent with, and enable interpretation of, preliminary experimental data. However, the models predict a stronger dependence of nanoparticle incorporation efficiency on functionalized charge density than measured in experiments, and do not completely capture a logarithmic growth phase seen in experimental light scatter. These discrepancies may suggest the presence of metastable disordered states in the experimental system. In addition to discussing future experiments for nanoparticle-capsid systems, we discuss broader implications for understanding assembly around charged cores such as nucleic acids.

Assistants on assembly tasks show great potential to benefit humans ranging from helping with everyday tasks to interacting in industrial settings. However, evaluation resources in assembly activities are underexplored. To foster system development, we propose a new multimodal QA evaluation dataset on assembly activities. Our dataset, ProMQA-Assembly, consists of 646 QA pairs that require multimodal understanding of human activity videos and their instruction manuals in an online-style manner. For cost effectiveness in the data creation, we adopt a semi-automated QA annotation approach, where LLMs generate candidate QA pairs and humans verify them. We further improve QA generation by integrating fine-grained action labels to diversify question types. Additionally, we create 81 instruction task graphs for our target assembly tasks. These newly created task graphs are used in our benchmarking experiment, as well as in facilitating the human verification process. With our dataset, we benchmark models, including competitive proprietary multimodal models. We find that ProMQA-Assembly contains challenging multimodal questions, where reasoning models showcase promising results. We believe our new evaluation dataset contributes to the further development of procedural-activity assistants.

Assembly theory bridges the gap between evolutionary biology and physics by providing a framework to quantify the generation and selection of novelty in biological systems. We formalize the assembly space as an acyclic digraph of strings with 2-in-regular assembly steps vertices and provide a novel definition of the assembly index. In particular, we show that the upper bound of the assembly index depends quantitatively on the number b of unit-length strings, and the longest length N of a string that has the assembly index of N − k is given by N(N−1) = b2 + b + 1 and by N(N−k) = b2 + b + 2k for 2 ≤ k ≤ 9. We also provide particular forms of such maximum assembly index strings. For k = 1, such odd-length strings are nearly balanced, and there are four such different strings if b = 2 and seventy-two if b = 3. We also show that each k copies of an n-plet contained in a string decrease its assembly index at least by k(n − 1) − a, where a is the assembly index of this n-plet. We show that the minimum assembly depth satisfies d min(N) = ⌈log2(N)⌉, for all b, and is the assembly depth of a maximum assembly index string. We also provide the general formula for the lengths of the minimum assembly index strings having only one independent assembly step in their assembly spaces. Since these results are also valid for b = 1, assembly theory subsumes information theory.