Related papers: Space-Efficient Bimachine Construction Based on th…
We present algorithmic results for the parallel assembly of many micro-scale objects in two and three dimensions from tiny particles, which has been proposed in the context of programmable matter and self-assembly for building high-yield…
We develop the theory of subproduct systems over the monoid $\mathbb{N}\times \mathbb{N}$, and the non-self-adjoint operator algebras associated with them. These are double sequences of Hilbert spaces $\{X(m,n)\}_{m,n=0}^\infty$ equipped…
A modification of the Adaptive Biasing Force method is introduced, in which the free energy is approximated by a sum of tensor products of one-dimensional functions. This enables to handle a larger number of reaction coordinates than the…
We show how up-to techniques for (bi-)similarity can be used in the setting of weighted systems. The problems we consider are language equivalence, language inclusion and the threshold problem (also known as universality problem) for…
Given a finite commutative monoid $M$, we show that submonoids of $M\times [n]$ - where $[n] = \{0,1,\ldots,n\}$ is equipped with the max operation $\vee$ - may be enumerated via the transfer matrix method. When $M$ is also idempotent, we…
We study monoidal transducers, transition systems arising as deterministic automata whose transitions also produce outputs in an arbitrary monoid, for instance allowing outputs to commute or to cancel out. We use the categorical framework…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
In this article we study how a subshift can simulate another one, where the notion of simulation is given by operations on subshifts inspired by the dynamical systems theory (factor, projective subaction...). There exists a correspondence…
We study the minimal thermodynamically consistent model for an adaptive machine that transfers particles from a higher chemical potential reservoir to a lower one. This model describes essentials of the inhomogeneous catalysis. It is…
Serial and parallel algorithms for simulation of tandem queueing systems with infinite buffers are presented, and their performance is examined. It is shown that the algorithms which are based on a simple computational procedure involve low…
Processing sets or other unordered, potentially variable-sized inputs in neural networks is usually handled by aggregating a number of input tensors into a single representation. While a number of aggregation methods already exist from…
Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they…
We prove that any Turing machine running on inputs of arbitrary length can be simulated by a constant bit-size transformer, as long as the context window is sufficiently long. This improves previous works, which require scaling up either…
In this work, we propose and study in depth a universal quantum computing architecture based on a quantum construction of transistors. Our teleportation-based quantum transistors, called ``telesistors'', are ground states of systems with…
In this paper, we present a multiplier based on a sequence of approximated accumulations. According to a given splitting point of the carry chains, the technique herein introduced allows varying the quality of the accumulations and,…
Theories of phase change and self-assembly often invoke the idea of a `quasiequilibrium', a regime in which the nonequilibrium association of building blocks results nonetheless in a structure whose properties are determined solely by an…
We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a…
We design the information-acquiring von Neumann architecture of a computer in a fine-grained or coarse-grained model of the registers (quickly accessible memories) in the central processing unit, where information is carried by classical…
For an arbitrary Euclidean building we define a certain combing, which satisfies the `fellow traveller property' and admits a recursive definition. Using this combing we prove that any group acting freely, cocompactly and by order…
We use some of the largest order statistics of the random projections of a reference signal to construct a binary embedding that is adapted to signals correlated with such signal. The embedding is characterized from the analytical…