228 research outputs found
Exact maximal reduction of stochastic reaction networks by species lumping
Motivation: Stochastic reaction networks are a widespread model to describe
biological systems where the presence of noise is relevant, such as in cell
regulatory processes. Unfortu-nately, in all but simplest models the resulting
discrete state-space representation hinders analytical tractability and makes
numerical simulations expensive. Reduction methods can lower complexity by
computing model projections that preserve dynamics of interest to the user.
Results: We present an exact lumping method for stochastic reaction networks
with mass-action kinetics. It hinges on an equivalence relation between the
species, resulting in a reduced network where the dynamics of each
macro-species is stochastically equivalent to the sum of the original species
in each equivalence class, for any choice of the initial state of the system.
Furthermore, by an appropriate encoding of kinetic parameters as additional
species, the method can establish equivalences that do not depend on specific
values of the parameters. The method is supported by an efficient algorithm to
compute the largest species equivalence, thus the maximal lumping. The
effectiveness and scalability of our lumping technique, as well as the physical
interpretability of resulting reductions, is demonstrated in several models of
signaling pathways and epidemic processes on complex networks. Availability:
The algorithms for species equivalence have been implemented in the software
tool ERODE, freely available for download from https://www.erode.eu
A recommendation system for CAD assembly modeling based on graph neural networks
In computer-aided design (CAD), software tools support design engineers during the modeling of assemblies, i.e., products that consist of multiple components. Selecting the right components is a cumbersome task for design engineers as they have to pick from a large number of possibilities. Therefore, we propose to analyze a data set of past assemblies composed of components from the same component catalog, represented as connected, undirected graphs of components, in order to suggest the next needed component. In terms of graph machine learning, we formulate this as graph classification problem where each class corresponds to a component ID from a catalog and the models are trained to predict the next required component. In addition to pretraining of component embeddings, we recursively decompose the graphs to obtain data instances in a self-supervised fashion without imposing any node insertion order. Our results indicate that models based on graph convolution networks and graph attention networks achieve high predictive performance, reducing the cognitive load of choosing among 2,000 and 3,000 components by recommending the ten most likely components with 82-92% accuracy, depending on the chosen catalog
Optimal Kullback-Leibler Aggregation via Information Bottleneck
In this paper, we present a method for reducing a regular, discrete-time
Markov chain (DTMC) to another DTMC with a given, typically much smaller number
of states. The cost of reduction is defined as the Kullback-Leibler divergence
rate between a projection of the original process through a partition function
and a DTMC on the correspondingly partitioned state space. Finding the reduced
model with minimal cost is computationally expensive, as it requires an
exhaustive search among all state space partitions, and an exact evaluation of
the reduction cost for each candidate partition. Our approach deals with the
latter problem by minimizing an upper bound on the reduction cost instead of
minimizing the exact cost; The proposed upper bound is easy to compute and it
is tight if the original chain is lumpable with respect to the partition. Then,
we express the problem in the form of information bottleneck optimization, and
propose using the agglomerative information bottleneck algorithm for searching
a sub-optimal partition greedily, rather than exhaustively. The theory is
illustrated with examples and one application scenario in the context of
modeling bio-molecular interactions.Comment: 13 pages, 4 figure
Probing the Structure and Photophysics of Porphyrinoid Systems for Functional Materials
Porphyrins (Pors) and their many cousins, including phthalocyanines (Pcs), corroles (Cors), subphthalocyanines (SubPcs), porphyrazines (Pzs), and naphthalocyanines (NPcs), play amazingly diverse roles in biological and non-biological systems because of their unique and tunable physical and chemical properties. These compounds, collectively known as porphyrinoids, can be employed in any number of functional devices that have the potential to address the challenges of modern society. Their incorporation into such devices, however, depends on many structural factors that must be well understood and carefully controlled in order to achieve the desired behavior. Self-assembly and self-organization are key processes for developing these new technologies, as they will allow for inexpensive, efficient, and scalable designs. The overall goal of this dissertation is to elucidate and ultimately control the interplay between the hierarchical structure and the photophysical properties of these kinds of systems. This includes several case studies concerning the design and spectroscopic analysis of supramolecular systems formed through simple, scalable synthetic methods. We also present detailed experimental and computational studies on some porphyrin and phthalocyanine compounds that provide evidence for fundamental changes in their molecular structure. In addition to their impact on the photophysics, these changes also have implications for the organization of these molecules into higher order materials and devices. It is our hope that these findings will help to drive chemists and engineers to look more closely at every level of hierarchical structure in the search for the next generation of advanced materials
Extending SQL for computing shortest paths
Reachability and shortest paths are among two of the most common queries realized on graphs. While graph frameworks and property graph databases provide an extensive and convenient built-in support for these operations, it is still both clunky and inefficient to perform on standard SQL DBMSs. In this paper, we present an extension to the standard SQL language to compute both reachability predicates and many-to-many shortest path queries. We first describe a methodology to represent a directed graph starting from virtual table expressions. Second, we introduce a new type of operator to compute shortest
Communities in temporal networks: from theoretical underpinnings to real-life applications
Static aggregations of network activity can unravel attributes of the complex systems they represent. However, they fall short when the structure of the systems changes over time. In some cases, changes are sluggish, such as in power grids, where lines enjoy a lengthy temporal permanence. In others, a high frequency of change is observed, such as on a network of online messages, social contacts, pathogen transmission or ball passing in a soccer game. In these cases, reducing what is inherently a temporal network to a static one, leads necessarily to a loss of information, such as causal relationships, precedence or reachability rules. Temporal networks are thus the main subject of this thesis, centered on the study of network evolution from the point of view of its clusters as significant meso-structures. The thesis has two interrelated parts. In the first, theoretical challenges are addressed and original algorithms, methods and tools are developed that can further the study of network theory. In the second, these developments are applied to the analysis of team invasion sports. A measurement of game dynamics was created based on a temporal network representation of a match, with nodes clustered by spatial proximity. These measurements were found to correlate with match events of known dynamics. Moreover, they reveal unique, multi-level, aspects of the game, from the individual players contributions, to the clusters of interacting players, to their teams and their matches, which is useful for game analysis, training and strategy development.As agregações estáticas das ligações de uma rede podem revelar atributos dos sistemas complexos que representam. Todavia, são insuficientes quando a estrutura dos sistemas se altera com o tempo. Em alguns casos, as transformações são lentas, tais como em redes de transmissão de eletricidade em que as linhas se mantêm inalteráveis por largos perÃodos de tempo. Noutras, regista-se uma taxa elevada de mudança, como por exemplo numa rede de mensagens em linha, contatos sociais, transmissão de patógenos ou passes num jogo de futebol. Nestes casos, reduzir o que é inerentemente uma rede temporal a uma rede estática, leva a uma perda de informação, tais como relações causais, regras de precedência ou de acessibilidade. Redes temporais são assim o tema desta tese, centrada nos seus agrupamentos, como meso-estruturas significantes. A tese está dividida em duas partes. Na primeira, são considerados problemas teóricos, e são desenvolvidos algoritmos, métodos e ferramentas que avançam o estudo da teoria de redes. Na segunda, estes desenvolvimentos são aplicados à análise de jogos desportivos coletivos de invasão. Foi criada uma medida de dinâmica do jogo, baseada na representação da partida através de uma rede temporal de nós agrupados por proximidade espacial. Os resultados obtidos correlacionam-se com eventos do jogo de dinâmica conhecida. Adicionalmente, esta medida revela aspetos únicos e multi-nÃvel da dinâmica do jogo, desde a contribuição individual do jogador, até aos agrupamentos de jogadores, da equipa e das partidas, útil para a análise do jogo, de treino e de desenvolvimento estratégico
Set-to-Sequence Methods in Machine Learning: A Review
Machine learning on sets towards sequential output is an important and
ubiquitous task, with applications ranging from language modelling and
meta-learning to multi-agent strategy games and power grid optimization.
Combining elements of representation learning and structured prediction, its
two primary challenges include obtaining a meaningful, permutation invariant
set representation and subsequently utilizing this representation to output a
complex target permutation. This paper provides a comprehensive introduction to
the field as well as an overview of important machine learning methods tackling
both of these key challenges, with a detailed qualitative comparison of
selected model architectures.Comment: 46 pages of text, with 10 pages of references. Contains 2 tables and
4 figure
Complex event types for agent-based simulation
This thesis presents a novel formal modelling language, complex event types (CETs), to describe behaviours
in agent-based simulations. CETs are able to describe behaviours at any computationally
represented level of abstraction. Behaviours can be specified both in terms of the state transition rules of
the agent-based model that generate them and in terms of the state transition structures themselves.
Based on CETs, novel computational statistical methods are introduced which allow statistical dependencies
between behaviours at different levels to be established. Different dependencies formalise
different probabilistic causal relations and Complex Systems constructs such as ‘emergence’ and ‘autopoiesis’.
Explicit links are also made between the different types of CET inter-dependency and the
theoretical assumptions they represent.
With the novel computational statistical methods, three categories of model can be validated and
discovered: (i) inter-level models, which define probabilistic dependencies between behaviours at different
levels; (ii) multi-level models, which define the set of simulations for which an inter-level model
holds; (iii) inferred predictive models, which define latent relationships between behaviours at different
levels.
The CET modelling language and computational statistical methods are then applied to a novel
agent-based model of Colonic Cancer to demonstrate their applicability to Complex Systems sciences
such as Systems Biology. This proof of principle model provides a framework for further development
of a detailed integrative model of the system, which can progressively incorporate biological data from
different levels and scales as these become available
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