Related papers: Computing Real Numbers with Large-Population Proto…
Population protocols are a formal model of computation by identical, anonymous mobile agents interacting in pairs. Their computational power is rather limited: Angluin et al. have shown that they can only compute the predicates over…
Determinantal Point Process (DPPs) are statistical models for repulsive point patterns. Both sampling and inference are tractable for DPPs, a rare feature among models with negative dependence that explains their popularity in machine…
Measures of wealth and production have been found to scale superlinearly with the population of a city. Therefore, it makes economic sense for humans to congregate together in dense settlements. A recent model of population dynamics showed…
We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories. In this model, distinguishable particles start out with known momenta and…
Population protocols are a model of computation in which indistinguishable mobile agents interact in pairs to decide a property of their initial configuration. Originally introduced by Angluin et. al. in 2004 with a constant number of…
We introduce a notion of algorithmic randomness for algebraic fields. We prove the existence of a continuum of algebraic extensions of $\mathbb{Q}$ that are random according to our definition. We show that there are noncomputable algebraic…
Comprehensively understanding and accurately predicting the performance of large language models across diverse downstream tasks has emerged as a pivotal challenge in NLP research. The pioneering scaling law on downstream works demonstrated…
We consider the product of determinantal point processes (DPPs), a point process whose probability mass is proportional to the product of principal minors of multiple matrices, as a natural, promising generalization of DPPs. We study the…
We study exact majority consensus in the population protocol model. In this model, the system is described by a graph $G = (V,E)$ with $n$ nodes, and in each time step, a scheduler samples uniformly at random a pair of adjacent nodes to…
Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…
This study develops an algorithm for distributed computing of linear programming problems of huge-scales. Global consensus with single common variable, multiblocks, and augmented Lagrangian are adopted. The consensus is used to partition…
We study uniform population protocols: networks of anonymous agents whose pairwise interactions are chosen at random, where each agent uses an identical transition algorithm that does not depend on the population size $n$. Many existing…
Population protocols are a model of distributed computing where $n$ agents, each a simple finite-state machine, interact in pairs to solve a common task against a (adversarial) interaction scheduler. This model was intensively studied in…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
Population protocols are a model for distributed computing that is focused on simplicity and robustness. A system of $n$ identical agents (finite state machines) performs a global task like electing a unique leader or determining the…
The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of…
Let $\{u_n\}_n$ be a non-degenerate linear recurrence sequence of integers with Binet's formula given by $u_n= \sum_{i=1}^{m} P_i(n)\alpha_i^n.$ Assume $\max_i \vert \alpha_i \vert >1$. In 1977, Loxton and Van der Poorten conjectured that…
We study determinantal point processes (DPP) through the lens of algebraic statistics. We count the critical points of the log-likelihood function, and we compute them for small models, thereby disproving a conjecture of Brunel, Moitra,…
We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length $\omega$ to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite…
Reversible Primitive Permutations (RPP) are recursively defined functions designed to model Reversible Computation. We illustrate a proof, fully developed with the proof-assistant Lean, certifying that: "RPP can encode every Primitive…