Related papers: Six Birds: Foundations of Emergence Calculus
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
We propose a globally exponentially convergent observer for the dynamical system evolving on matrix Lie groups with bounded velocity with unknown bound. We design the observer in the ambient Euclidean space and show exponential convergence…
Autonomous morphology, such as inflection class systems and paradigmatic distribution patterns, is widespread and diachronically resilient in natural language. Why this should be so has remained unclear given that autonomous morphology…
We introduce and study exterior distance function (EDF) and correspondent exterior point method (EPM) for convex optimization. The EDF is a classical Lagrangian for an equivalent problem obtained from the initial one by monotone…
We propose an exact iterative algorithm for minimization of a class of continuous cell-wise linear convex functions on a hyperplane arrangement. Our particular setup is motivated by evaluation of so-called rank estimators used in robust…
The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the…
We bound the time it takes for a group of birds to reach steady state in a standard flocking model. We prove that (i) within single exponential time fragmentation ceases and each bird settles on a fixed flying direction; (ii) the flocking…
Modular reasoning about class invariants is challenging in the presence of dependencies among collaborating objects that need to maintain global consistency. This paper presents semantic collaboration: a novel methodology to specify and…
We provide a bird's eye view onto the area of sequential change-point detection. We focus on the discrete-time case with known pre- and post-change data distributions and offer a summary of the forefront asymptotic results established in…
Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In…
We extend to $p$-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise $\alpha$-averaged mappings. Our main…
The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentions of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms. In each case it…
Probabilistic knowledge graph embeddings represent entities as distributions, using learned variances to quantify epistemic uncertainty. We identify a fundamental limitation: these variances are relation-agnostic, meaning an entity receives…
In this paper we investigate fixed-point numbers and entropies of endomorphisms on abelian varieties. It was shown quite recently that the number of fixed-points of an iterated endomorphism on a simple complex torus is either periodic or…
Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms…
This dissertation makes three main contributions. First, We identify a new connection between policy gradient and dynamic programming in MMDPs and propose the Coordinate Ascent Dynamic Programming (CADP) algorithm to compute a Markov policy…
"Emergence", the phenomenon where a complex system displays properties, behaviours, or dynamics not trivially reducible to its constituent elements, is one of the defining properties of complex systems. Recently, there has been a concerted…
This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…
Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this…
We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to…