Related papers: The one-way function based on computational uncert…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
The existence of one-way functions is arguably the most important problem in computer theory. The article discusses and refines a number of concepts relevant to this problem. For instance, it gives the first combinatorial complete owf,…
We consider a distributed function computation problem in which parties observing noisy versions of a remote source facilitate the computation of a function of their observations at a fusion center through public communication. The…
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore…
The pinch technique (PT) is an algorithm for the rearrangement of contributions to conventional, gauge-dependent n-point functions in gauge theories to obtain a formulation of one-loop perturbation theory in terms of ``effective'' n-point…
A novel perspective on the design of robust model predictive control (MPC) methods is presented, whereby closed-loop constraint satisfaction is ensured using recursive feasibility of the MPC optimization. Necessary and sufficient conditions…
Cyclic and non-wellfounded proofs are now increasingly employed to establish metalogical results in a variety of settings, in particular for type systems with forms of (co)induction. Under the Curry-Howard correspondence, a cyclic proof can…
Exploiting previous results on Markovian dynamics and fluctuation theorems, we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach. The entropy production along single…
The increase in data traffic on the internet has significantly increased the relevance of data and image encryption. Among the techniques most used in cryptography, chaotic systems have received great attention due to their easy…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
We illustrate that, like the truncation error, the round-off error has a significant influence on the reliability of numerical simulations of chaotic dynamic systems. Due to the butterfly-effect, all numerical approaches in double precision…
Random features is a powerful universal function approximator that inherits the theoretical rigor of kernel methods and can scale up to modern learning tasks. This paper views uncertain system models as unknown or uncertain smooth functions…
Machine learning on encrypted data has received a lot of attention thanks to recent breakthroughs in homomorphic encryption and secure multi-party computation. It allows outsourcing computation to untrusted servers without sacrificing…
Equational reasoning is among the most important tools that functional programming provides us. Curiously, relatively less attention has been paid to reasoning about monadic programs. In this report we derive a backtracking algorithm for…
Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities,…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
The paper compares two generic techniques for deriving lower bounds and impossibility results in distributed computing. First, we prove a speedup theorem (a-la Brandt, 2019), for wait-free colorless algorithms, aiming at capturing the…
The Model-X knockoff procedure has recently emerged as a powerful approach for feature selection with statistical guarantees. The advantage of knockoff is that if we have a good model of the features X, then we can identify salient features…
The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function…
We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating…