21 research outputs found
Anomalous diffusion : from life to machines
Diffusion refers to numerous phenomena, by which particles and bodies of all kinds move throughout any kind of material, has emerged as one of the most prominent subjects in the study of complex systems. Motivated by the recent developments in experimental techniques, the field had an important burst in theoretical research, particularly in the study of the motion of particles in biological environments. Just with the information retrieved from the trajectories of particles we are now able to characterize many properties of the system with astonishing accuracy. For instance, when Einstein introduced the diffusion theory back in 1905, he used the motion of microscopic particles to calculate the size of the atoms of the liquid these were suspended. Initially, most of the experimental evidence showed that such systems follow Brownian-like dynamics, i.e. the homogeneous interaction between the particles and the environment led to its stochastic, but uncorrelated motion. However, we know now that such a simple explanation lacks crucial phenomena that have been shown to arise in a plethora of physical systems. The divergence from Brownian dynamics led to the theory of anomalous diffusion, in which the particles are affected in a way or another by their interactions with the environment such that their diffusion changes drastically. For instance features such as ergodicity, Gaussianity, or ageing are now crucial for in the understanding of diffusion processes, well beyond Brownian motion.
In theoretical terms, anomalous diffusion has a well-developed framework, able to explain most of the current experimental observations. However, it has been usually focused in describing the systems in terms of its macroscopic behaviour. This means that the processes are described by means of general models, able to predict the average or collective features. Even though such an approach leads to a correct description of the system and hints on the actual underlying phenomena, it lacks the understanding of the particular microscopic interactions leading to anomalous diffusion.
The work presented in this Thesis has two main goals. First, we will explore how one may use microscopical (or phenomenological) models to understand anomalous diffusion. By microscopical model we refer to a model in which we will set exactly how the interactions between the various components of a system are. Then, we will explore how these interactions may be tuned in order to recover and control anomalous diffusion and how its features depend on the properties of the system. We will explore crucial topics arising in recent experimental observations, such as weak-ergodicity breaking or liquid-liquid phase separation. Second, we will survey the topic of trajectory characterization. Even if our theories are extremely well developed, without an accurate tool for studying the trajectories observed in experiments, we will be unable to correctly make any faithful prediction. In particular, we will introduce one of the first machine learning techniques that can be used for such purpose, even in systems where previous techniques failed largely.La difusi贸n es el fen贸meno por el cual part铆culas de todas formas y tama帽os se mueven a trav茅s del entorno que les rodea. Su estudio se ha convertido en una potente herramienta para entender el comportamiento de sistemas complejos. Gracias al reciente desarrollo de diferentes t茅cnicas experimentales, este fen贸meno ha generado un enorme inter茅s tanto desde el punto de vista experimental como del te贸rico, y en especial,en el estudio del movimiento de part铆culas microsc贸picas en entornos biol贸gicos. Mediante el an谩lisis de las trayectorias de estas part铆culas, no solo somos capaces de caracterizar sus propiedades, sino tambi茅n las de su entorno. El propio Albert Einstein, autor junto con Marian Smoluchowski de la teor铆a de la difusi贸n, demostr贸 que era posible calcular el radio de los 谩tomos de un l铆quido simplemente mediante el an谩lisis del movimiento de una part铆cula suspendida en este. Esta teor铆a, que dio origen a lo que hoy conocemos como movimiento Browniano, consideraba que la interacci贸n homog茅nea de una part铆cula con su entorno provocaba el movimiento aleatorio de esta 煤ltima. Aunque el movimiento Browniano haya sido utilizado para describir una enorme cantidad de experimentos, hoy sabemos que existen sistemas particulares que se desv铆an de sus predicciones. Esta divergencia ha dado pie al desarrollo de la teor铆a de la difusi贸n an贸mala, en la que, debido a las propiedades de las part铆culas y sus entornos, la difusi贸n difiere dr谩sticamente de las predicciones de la teor铆a Browniana. Algunos fen贸menos como la ergodicidad, Gausianidad o el envejecimiento de difusi贸n, particulares de la difusi贸n an贸mala, son hoy en d铆a cruciales para entender el movimiento de part铆culas en sistemas complejos. En t茅rminos te贸ricos, la difusi贸n an贸mala tiene unas bases firmes, con las cu谩les se explica gran parte de las observaciones experimentales m谩s recientes. Esta teor铆a, sin embargo, suele centrarse en la descripci贸n de la difusi贸n desde un punto de vista macrosc贸pico. Esto quiere decir: analizar un sistema mediante modelos generales, capaces de predecir propiedades colectivas o globales. Aunque las teor铆as macrosc贸picas consiguen describir correctamente la mayor铆a de los procesos de difusi贸n, no tienen la capacidad de discernir qu茅 tipo de interacciones dan lugar a la difusi贸n an贸mala. El trabajo presentado en esta tesis tiene dos objetivos principales. El primero es explorar el uso de modelos microsc贸picos (o fenomenol贸gicos) para entender la difusi贸n an贸mala. Un modelo microsc贸pico, en contraposici贸n al macrosc贸pico, describe el sistema a partir de sus propiedades espec铆ficas. En este caso, a partir del tipo de interacciones que existen entre las part铆culas y su entorno. El objetivo es por lo tanto entender cu谩les de estas interacciones producen difusi贸n an贸mala. Adem谩s, caracterizaremos los par谩metros macrosc贸picos de la difusi贸n, como el exponente an贸malo, y mostraremos como depende de las propiedades del sistema. En el camino, exploraremos c贸mo fen贸menos como la rotura d茅bil de la ergodicidad (weak-ergodicity breaking) o la separaci贸n de fase aparecen en sistemas con interacciones complejas. El segundo objetivo consiste en el desarrollo de t茅cnicas para la caracterizaci贸n de trayectorias provenientes de procesos de difusi贸n. Aunque nuestro entendimiento te贸rico llegue a niveles insospechados en los pr贸ximos a帽os, sin un an谩lisis correcto y preciso de las trayectorias experimentales, jam谩s podremos construir un puente entre teor铆a y experimentos. Por tanto, el desarrollo de t茅cnicas con las que analizar con la mayor precisi贸n posible dichas trayectorias es un problema igual de importante que el desarrollo te贸rico de la difusi贸n. En este trabajo, estudiaremos c贸mo las t茅cnicas de aprendizaje autom谩tico (Machine Learning) pueden ser utilizadas para caracterizar dichas trayectorias, llegando a niveles de precisi贸n y an谩lisis muy por encim
Certificates of quantum many-body properties assisted by machine learning
Computationally intractable tasks are often encountered in physics and
optimization. Such tasks often comprise a cost function to be optimized over a
so-called feasible set, which is specified by a set of constraints. This may
yield, in general, to difficult and non-convex optimization tasks. A number of
standard methods are used to tackle such problems: variational approaches focus
on parameterizing a subclass of solutions within the feasible set; in contrast,
relaxation techniques have been proposed to approximate it from outside, thus
complementing the variational approach by providing ultimate bounds to the
global optimal solution. In this work, we propose a novel approach combining
the power of relaxation techniques with deep reinforcement learning in order to
find the best possible bounds within a limited computational budget. We
illustrate the viability of the method in the context of finding the ground
state energy of many-body quantum systems, a paradigmatic problem in quantum
physics. We benchmark our approach against other classical optimization
algorithms such as breadth-first search or Monte-Carlo, and we characterize the
effect of transfer learning. We find the latter may be indicative of phase
transitions, with a completely autonomous approach. Finally, we provide tools
to generalize the approach to other common applications in the field of quantum
information processing.Comment: 22 pages (12.5 + appendices), 8 figure
Optimal foraging strategies can be learned
The foraging behavior of animals is a paradigm of target search in nature.
Understanding which foraging strategies are optimal and how animals learn them
are central challenges in modeling animal foraging. While the question of
optimality has wide-ranging implications across fields such as economy,
physics, and ecology, the question of learnability is a topic of ongoing debate
in evolutionary biology. Recognizing the interconnected nature of these
challenges, this work addresses them simultaneously by exploring optimal
foraging strategies through a reinforcement learning framework. To this end, we
model foragers as learning agents. We first prove theoretically that maximizing
rewards in our reinforcement learning model is equivalent to optimizing
foraging efficiency. We then show with numerical experiments that, in the
paradigmatic model of non-destructive search, our agents learn foraging
strategies which outperform the efficiency of some of the best known strategies
such as L\'evy walks. These findings highlight the potential of reinforcement
learning as a versatile framework not only for optimizing search strategies but
also to model the learning process, thus shedding light on the role of learning
in natural optimization processes.Comment: 12 pages (6 main text) and 9 figures. Codes and tutorials available
at: https://gorkamunoz.github.io/rl_opts
Learning minimal representations of stochastic processes with variational autoencoders
Stochastic processes have found numerous applications in science, as they are
broadly used to model a variety of natural phenomena. Due to their intrinsic
randomness and uncertainty, they are however difficult to characterize. Here,
we introduce an unsupervised machine learning approach to determine the minimal
set of parameters required to effectively describe the dynamics of a stochastic
process. Our method builds upon an extended -variational autoencoder
architecture. By means of simulated datasets corresponding to paradigmatic
diffusion models, we showcase its effectiveness in extracting the minimal
relevant parameters that accurately describe these dynamics. Furthermore, the
method enables the generation of new trajectories that faithfully replicate the
expected stochastic behavior. Overall, our approach enables for the autonomous
discovery of unknown parameters describing stochastic processes, hence
enhancing our comprehension of complex phenomena across various fields.Comment: 9 pages, 5 figures, 1 table. Code available at
https://github.com/GabrielFernandezFernandez/SPIVA
Inferring pointwise diffusion properties of single trajectories with deep learning
In order to characterize the mechanisms governing the diffusion of particles
in biological scenarios, it is essential to accurately determine their
diffusive properties. To do so, we propose a machine learning method to
characterize diffusion processes with time-dependent properties at the
experimental time resolution. Our approach operates at the single-trajectory
level predicting the properties of interest, such as the diffusion coefficient
or the anomalous diffusion exponent, at every time step of the trajectory. In
this way, changes in the diffusive properties occurring along the trajectory
emerge naturally in the prediction, and thus allow the characterization without
any prior knowledge or assumption about the system. We first benchmark the
method on synthetic trajectories simulated under several conditions. We show
that our approach can successfully characterize both abrupt and continuous
changes in the diffusion coefficient or the anomalous diffusion exponent.
Finally, we leverage the method to analyze experiments of single-molecule
diffusion of two membrane proteins in living cells: the pathogen-recognition
receptor DC-SIGN and the integrin . The analysis allows us to
characterize physical parameters and diffusive states with unprecedented
accuracy, shedding new light on the underlying mechanisms.Comment: 17 pages, 9 figures, 1 table. Code is found in
https://github.com/BorjaRequena/ste
Efficient training of energy-based models via spin-glass control
[EN] We introduce a new family of energy-based probabilistic graphical models for efficient unsupervised learning. Its definition is motivated by the control of the spin-glass properties of the Ising model described by the weights of Boltzmann machines. We use it to learn the Bars and Stripes dataset of various sizes and the MNIST dataset, and show how they quickly achieve the performance offered by standard methods for unsupervised learning. Our results indicate that the standard initialization of Boltzmann machines with random weights equivalent to spin-glass models is an unnecessary bottleneck in the process of training. Furthermore, this new family allows for very easy access to low-energy configurations, which points to new, efficient training algorithms. The simplest variant of such algorithms approximates the negative phase of the log-likelihood gradient with no Markov chain Monte Carlo sampling costs at all, and with an accuracy sufficient to achieve good learning and generalization.ML and AA groups acknowledge the Spanish Ministry MINECO and State Research Agency AEI (FIDEUA PID2019-106901GBI00/10.13039/501100011033, Severo Ochoa Grant Nos. SEV-2015-0522 and CEX2019-000910-S, FPI), the European Social Fund, Fundacio Cellex, Fundacio Mir-Puig, Generalitat de Catalunya (AGAUR Grant Nos. 2017 SGR 1341 and SGR 1381, CERCA program, QuantumCAT U16-011424, co-funded by ERDF Operational Program of Catalonia 2014-2020), ERC AdG NOQIA and CERQUTE, EU FEDER, MINECO-EU QUANTERA MAQS (funded by the State Research Agency AEI PCI2019-111828-2/10.13039/501100011033), the National Science Centre, Poland-Symfonia Grant No. 2016/20/W/ST4/00314 and the AXA Chair in Quantum Information Science. A P-K acknowledges funding from Fundacio Obra Socialla Caixa' (LCF/BQ/ES15/10360001) and the European Union's Horizon 2020 research and innovation programme-Grant Agreement No. 648913. G M-G acknowledges funding from Fundacio Obra Social 'la Caixa' (LCF-ICFO grant). M A G-M acknowledges funding from the Spanish Ministry of Education and Vocational Training (MEFP) through the Beatriz Galindo program 2018 (BEAGAL18/00203).Pozas-Kerstjens, A.; Mu帽oz-Gil, G.; Pi帽ol, E.; Garcia March, MA.; Ac铆n, A.; Lewenstein, M.; Grzybowski, PR. (2021). Efficient training of energy-based models via spin-glass control. Machine Learning: Science and Technology. 2(2). https://doi.org/10.1088/2632-2153/abe8070250262
Quantitative evaluation of methods to analyze motion changes in single-particle experiments
The analysis of live-cell single-molecule imaging experiments can reveal
valuable information about the heterogeneity of transport processes and
interactions between cell components. These characteristics are seen as motion
changes in the particle trajectories. Despite the existence of multiple
approaches to carry out this type of analysis, no objective assessment of these
methods has been performed so far. Here, we have designed a competition to
characterize and rank the performance of these methods when analyzing the
dynamic behavior of single molecules. To run this competition, we have
implemented a software library to simulate realistic data corresponding to
widespread diffusion and interaction models, both in the form of trajectories
and videos obtained in typical experimental conditions. The competition will
constitute the first assessment of these methods, provide insights into the
current limits of the field, foster the development of new approaches, and
guide researchers to identify optimal tools for analyzing their experiments.Comment: 19 pages, 4 figure, 2 tables. Stage 1 registered report, accepted in
principle in Nature Communications
(https://springernature.figshare.com/articles/journal_contribution/Quantitative_evaluation_of_methods_to_analyze_motion_changes_in_single-particle_experiments_Registered_Report_Stage_1_Protocol_/24771687
Universal representation by Boltzmann machines with Regularised Axons
It is widely known that Boltzmann machines are capable of representing
arbitrary probability distributions over the values of their visible neurons,
given enough hidden ones. However, sampling -- and thus training -- these
models can be numerically hard. Recently we proposed a regularisation of the
connections of Boltzmann machines, in order to control the energy landscape of
the model, paving a way for efficient sampling and training. Here we formally
prove that such regularised Boltzmann machines preserve the ability to
represent arbitrary distributions. This is in conjunction with controlling the
number of energy local minima, thus enabling easy \emph{guided} sampling and
training. Furthermore, we explicitly show that regularised Boltzmann machines
can store exponentially many arbitrarily correlated visible patterns with
perfect retrieval, and we connect them to the Dense Associative Memory
networks.Comment: 12 pages. Updated reference
Dysregulated FOXO1 activity drives skeletal muscle intrinsic dysfunction in amyotrophic lateral sclerosis
Amyotrophic Lateral Sclerosis (ALS) is a multisystemic neurodegenerative disorder, with accumulating evidence indicating metabolic disruptions in the skeletal muscle preceding disease symptoms, rather than them manifesting as a secondary consequence of motor neuron (MN) degeneration. Hence, energy homeostasis is deeply implicated in the complex physiopathology of ALS and skeletal muscle has emerged as a key therapeutic target. Here, we describe intrinsic abnormalities in ALS skeletal muscle, both in patient-derived muscle cells and in muscle cell lines with genetic knockdown of genes related to familial ALS, such as TARDBP (TDP-43) and FUS. We found a functional impairment of myogenesis that parallels defects of glucose oxidation in ALS muscle cells. We identified FOXO1 transcription factor as a key mediator of these metabolic and functional features in ALS muscle, via gene expression profiling and biochemical surveys in TDP-43 and FUS-silenced muscle progenitors. Strikingly, inhibition of FOXO1 mitigated the impaired myogenesis in both the genetically modified and the primary ALS myoblasts. In addition, specific in vivo conditional knockdown of TDP-43 or FUS orthologs (TBPH or caz) in Drosophila muscle precursor cells resulted in decreased innervation and profound dysfunction of motor nerve terminals and neuromuscular synapses, accompanied by motor abnormalities and reduced lifespan. Remarkably, these phenotypes were partially corrected by foxo inhibition, bolstering the potential pharmacological management of muscle intrinsic abnormalities associated with ALS. The findings demonstrate an intrinsic muscle dysfunction in ALS, which can be modulated by targeting FOXO factors, paving the way for novel therapeutic approaches that focus on the skeletal muscle as complementary target tissue
Modern applications of machine learning in quantum sciences
In these Lecture Notes, we provide a comprehensive introduction to the most
recent advances in the application of machine learning methods in quantum
sciences. We cover the use of deep learning and kernel methods in supervised,
unsupervised, and reinforcement learning algorithms for phase classification,
representation of many-body quantum states, quantum feedback control, and
quantum circuits optimization. Moreover, we introduce and discuss more
specialized topics such as differentiable programming, generative models,
statistical approach to machine learning, and quantum machine learning.Comment: 268 pages, 87 figures. Comments and feedback are very welcome.
Figures and tex files are available at
https://github.com/Shmoo137/Lecture-Note