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The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering experimental results. It enables us to improve the description…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
The statistical methods derived and described in this thesis provide new ways to elucidate the structural properties of text and other symbolic sequences. Generically, these methods allow detection of a difference in the frequency of a…
Pyrosequencing is emerging as one of the important next-generation sequencing technologies. We derive the statistical distributions of this technique in terms of nucleotide probabilities of the target sequences. We give exact distributions…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the…
We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk problem through a new analytical technique, based on invariance under generalized cutting-decimation transformations. These fractals are…
We describe a formal approach based on graphical causal models to identify the "root causes" of the change in the probability distribution of variables. After factorizing the joint distribution into conditional distributions of each…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
Information cascades are ubiquitous in both physical society and online social media, taking on large variations in structures, dynamics and semantics. Although the dynamics and semantics of information cascades have been studied, the…
Mathematical models are fundamental building blocks in the design of dynamical control systems. As control systems are becoming increasingly complex and networked, approaches for obtaining such models based on first principles reach their…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
The robustness of fault detection algorithms against uncertainty is crucial in the real-world industrial environment. Recently, a new probabilistic design scheme called distributionally robust fault detection (DRFD) has emerged and received…
Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…
Standard formulations of supervenience typically treat higher level properties as point valued facts strictly fixed by underlying base states. However, in many scientific domains, from statistical mechanics to machine learning, basal…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We review the application of Statistical Mechanics methods to the study of online learning of a drifting concept in the limit of large systems. The model where a feed-forward network learns from examples generated by a time dependent…
The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of…
Modern encryption algorithms form the foundation of digital security. However, the widespread use of encryption algorithms results in significant challenges for network defenders in identifying which specific algorithms are being employed.…
In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.