Related papers: On the Number of Observation Nodes in Boolean Netw…

Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable. The size of the connected components…

How to observe the state of a network from a limited number of measurements has become an important issue in complex networks, engineering, communication, epidemiology, etc. Under some scenarios, it is neither unfeasible nor unnecessary to…

In an entanglement swapping scenario, if two sources sharing entangled states between three parties are independent, local correlations lead to a different kind of inequalities than the standard Bell inequalities, known as network local…

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…

The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…

A Boolean network (BN) with $n$ components is a discrete dynamical system described by the successive iterations of a function $f:\{0,1\}^n\to\{0,1\}^n$. In most applications, the main parameter is the interaction graph of $f$: the digraph…

We call a system super-linearizable if it admits finite-dimensional embedding as a linear system -- known as a finite-dimensional Koopman embedding; said otherwise, if its dynamics can be linearized by adding a finite set of observables. We…

An observability condition number is defined for physical systems modeled by network dynamics. Assuming the dynamical equations of the network are known and a noisy trajectory is observed at a subset of the nodes, we calculate the expected…

Boolean networks have been used successfully in modeling biological networks and provide a good framework for theoretical analysis. However, the analysis of large networks is not trivial. In order to simplify the analysis of such networks,…

The concept of observability of linear systems initiated with Kalman in the mid 1950s. Roughly a decade later, the observability of nonlinear systems appeared. By such definitions a system is either observable or not. Continuous measures of…

Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…

Studies of networked phenomena, such as interactions in online social media, often rely on incomplete data, either because these phenomena are partially observed, or because the data is too large or expensive to acquire all at once.…

Detecting which nodes in graphs are outliers is a relatively new machine learning task with numerous applications. Despite the proliferation of algorithms developed in recent years for this task, there has been no standard comprehensive…

AND-OR networks are Boolean networks where each coordinate function is either the AND or OR logical operator. We study the number of fixed points of these Boolean networks in the case that they have a wiring diagram with chain topology. We…

We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We…

This study investigates measurement strategies in a scenario where multiple pairs of Alices and Bobs independently and sequentially observe entangled states. The aim is to maximize the number of observer pairs $(A_k,B_l)$ that can witness…

Boolean networks (BNs) are widely used to model the qualitative dynamics of biological systems. Besides the logical rules determining the evolution of each component with respect to the state of its regulators, the scheduling of component…

An important issue in neural network research is how to choose the number of nodes and layers such as to solve a classification problem. We provide new intuitions based on earlier results by An et al. (2015) by deriving an upper bound on…

Batch Normalization (BN) techniques have been proposed to reduce the so-called Internal Covariate Shift (ICS) by attempting to keep the distributions of layer outputs unchanged. Experiments have shown their effectiveness on training deep…

Regulatory networks (RNs) are a well-accepted modelling formalism in computational systems biology. The control of RNs is currently receiving a lot of attention because it provides a computational basis for cell reprogramming -- an…