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Bayesian network (BN) modelling is extensively used in systems epidemiology. Usually it consists in selecting and reporting the best-fitting structure conditional to the data. A major practical concern is avoiding overfitting, on account of…

We consider the problem of deterministic load balancing of tokens in the discrete model. A set of $n$ processors is connected into a $d$-regular undirected network. In every time step, each processor exchanges some of its tokens with each…

In this thesis, branching Brownian motion (BBM) is a random particle system where the particles diffuse on the real line according to Brownian motions and branch at constant rate into a random number of particles with expectation greater…

In using the Bayesian network (BN) to construct the complex multistate system's reliability model as described in Part I, the memory storage requirements of the node probability table (NPT) will exceed the random access memory (RAM) of the…

Ensuring that the right resource is available at the right location and time remains a major challenge for organizations operating large-scale logistics networks. The challenge comes from uneven demand patterns and the resulting asymmetric…

In an increasingly complex scenario for network management, a solution that allows configuration in more autonomous way with less intervention of the network manager is expected. This paper presents an evaluation of similarity functions…

Bayesian multinomial logistic-normal (MLN) models are popular for the analysis of sequence count data (e.g., microbiome or gene expression data) due to their ability to model multivariate count data with complex covariance structure.…

Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing…

We extend Probability Bracket Notation (PBN), inspired by the Dirac notation in quantum mechanics, to multivariable probability systems and static Bayesian networks (BNs). By defining probability distributions and conditional expectations…

Large language models (LLMs) are increasingly explored for their reasoning capabilities, yet their ability to perform structured, constraint-based optimization from natural language remains insufficiently understood. This study evaluates…

We consider two variational models for transport networks, an urban planning and a branched transport model, in both of which there is a preference for networks that collect and transport lots of mass together rather than transporting all…

The martingale part in the semimartingale decomposition of a Brownian motion with respect to an enlargement of its filtration, is an anticipative mapping of the given Brownian motion. In analogy to optimal transport theory, we define causal…

Analysis of large data collections using popular machine learning and statistical algorithms has been a topic of increasing research interest. A typical analysis workload consists of applying an algorithm to build a model on a data…

The performance of a neural network for a given task is largely determined by the initial calibration of the network parameters. Yet, it has been shown that the calibration, also referred to as training, is generally NP-complete. This…

Training and running deep neural networks (NNs) often demands a lot of computation and energy-intensive specialized hardware (e.g. GPU, TPU...). One way to reduce the computation and power cost is to use binary weight NNs, but these are…

We reinterpret some online greedy algorithms for a class of nonlinear "load-balancing" problems as solving a mathematical program online. For example, we consider the problem of assigning jobs to (unrelated) machines to minimize the sum of…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory…

We consider a queueing network operating under a strictly upper-triangular routing matrix with per column at most one non-negative entry. The root node is fed by a Gaussian process with stationary increments. Our aim is to characterize the…

Closed queuing networks with finite capacity buffers and skip-over policies are fundamental models in the performance evaluation of computer and communication systems. This technical report presents the details of computational algorithms…