Related papers: Time and Space Bounds for Reversible Simulation
The emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and…
Algorithmic \emph{replicability} has recently been introduced to address the need for reproducible experiments in machine learning. A \emph{replicable online learning} algorithm is one that takes the same sequence of decisions across…
Natural disasters may have considerable impact on society as well as on (re)insurance industry. Max-stable processes are ideally suited for the modeling of the spatial extent of such extreme events, but it is often assumed that there is no…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
The subspace approximation problem Subspace($k$,$p$) asks for a $k$-dimensional linear subspace that fits a given set of points optimally, where the error for fitting is a generalization of the least squares fit and uses the $\ell_{p}$ norm…
Reversible computation opens up the possibility of overcoming some of the hardware's current physical limitations. It also offers theoretical insights, as it enriches multiple paradigms and models of computation, and sometimes…
The completeness of quantum mechanics in predictive power is a central question in its foundational study. While most investigations focus on two-dimensional systems, high-dimensional systems are more general and widely applicable. Building…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We ask how much energy is required to weakly simulate an $n$-qubit quantum circuit (i.e., produce samples from its output distribution) by a unitary circuit in a hybrid qubit-oscillator model. The latter consists of a certain number of…
We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability…
We derive information-theoretic converses (i.e., lower bounds) for the minimum time required by any algorithm for distributed function computation over a network of point-to-point channels with finite capacity, where each node of the…
The greedy spanner is the highest quality geometric spanner (in e.g. edge count and weight, both in theory and practice) known to be computable in polynomial time. Unfortunately, all known algorithms for computing it take Omega(n^2) time,…
In the paradigm of thermodynamic computing, instead of behaving deterministically, hardware undergoes a stochastic process in order to sample from a distribution of interest. While it has been hypothesized that thermodynamic computers may…
We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal…
Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…
Non-reversible lifts reduce the relaxation time of reversible diffusions at most by a square root. For reversible diffusions on domains in Euclidean space, or, more generally, on a Riemannian manifold with boundary, non-reversible lifts are…
We derive general bounds on the probability that the empirical first-passage time $\overline{\tau}_n\equiv \sum_{i=1}^n\tau_i/n$ of a reversible ergodic Markov process inferred from a sample of $n$ independent realizations deviates from the…
The continuation of Misner space into the Euclidean region is seen to imply the topological restriction that the period of the closed spatial direction becomes time-dependent. This restriction results in a modified Lorentzian Misner space…
The aim of this contribution is twofold. First, we show that when two (or more) different quantum groups share the same noncommutative spacetime, such an 'ambiguity' can be resolved by considering together their corresponding noncommutative…