22 papers · ranked by Valyu relevance
Jonathan E. W. Huffmann, Holger Boche
Rate distortion theory treats the problem of encoding a source with minimum codebook size while at the same time allowing for a certain amount of errors in the reconstruction measured by a fidelity criterion and distortion level. Similar to the channel coding problem the optimal rate of the codebook with respect to the…
K. L. Kirkpatrick
The theoretical foundation of neuroscience differs from that of artificial intelligence, and to bridge this gap with AI, we would need a new computing paradigm that describes both fields well. The gap came from mathematicians’ invention of computability theory, which was deliberately narrower than cognition and yet…
Suzanne Boyd, Christian Wolf
We study the computability of Julia sets for polynomial diffeomorphisms of $\mathbb{C}^2$ with dynamical degree $d>1$, whose prototypical examples are complex Hénon maps. In previous work, we established computability under the assumption of hyperbolicity (Axiom A). Here, we extend this result to maps whose Fatou…
Jeff Edmonds, Ming Li
Kolmogorov complexity asks whether a string can be outputted by a Turing Machine (TM) whose description is shorter. Analogously, a real number is considered computable if a Turing machine can generate its decimal expansion. The modern $ϵ$-approximation definition of computability, widely used in practical computation…
Baruch Garcia
We already know that several problems like the inequivalence of P and EXP as well as the undecidability of the acceptance problem and halting problem relativize. However, relativization is a limited tool which cannot separate other complexity classes. What has not been proven explicitly is whether the…
Abrahim Ladha, Yiran Luo, Alan Tian
While the Church-Turing thesis asserts that effective calculability explicates to sets decidable by a Turing machine, the Cobham-Edmonds thesis asserts that feasible computation explicates to the complexity class $\mathsf{P}$, those decidable by a polynomial-time bounded Turing machine. The Church-Turing thesis has…
Georgios Mappouras, Charalambos Rossides
In recent years we observed rapid and significant advancements in artificial intelligence (A.I.). So much so that many wonder how close humanity is to developing an A.I. model that can achieve human level of intelligence, also known as artificial general intelligence (A.G.I.). In this work we look at this question and…
Francesco Caravelli, Jean-Charles Delvenne
We develop a Koopman operator framework for studying the computational properties of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a "Koopman halting problem that is recursively enumerable in general. For symbolic systems, such as…
Daniel Gahler, Dean Thomas, Slawomir Lach, Leroy Cronin
Complete Chemputer Authors: Daniel Gahler, Dean Thomas, Slawomir Lach, Leroy Cronin The most fundamental abstraction underlying all modern computers is the Turing Machine, that is, if any modern computer can simulate a Turing Machine, an equivalence which is called “Turing completeness”, it is theoretically possible to…
Daniel Puthawala, Brendan Reardon, Lawrence Babb, Kori Kuzma + 10 more
Categorical variants, or sets of genomic alterations constrained by shared properties, are pervasive across clinical, regulatory, and research domains in the biomedical ecosystem, yet their inconsistent and non-computable representation hinders data interoperability and clinical interpretation. We surveyed genomic…
Akihito Kajikawa, Masamori Kaku, Takayuki Kihara, Satoshi Nakata
In recent years, there has been rapid development in the foundational study of oracle computability from the perspective of Lawvere-Tierney topologies and their sheaves. In this article, we formulate and analyze the notion of reducibility within the framework of total computability. Then, using sheaf subtoposes derived…
Robert Worden
This paper uses simple arguments to derive a negative conclusion: that a computer cannot be conscious. If the brain is only a neural computer, brains cannot be conscious. Consciousness implies that there is something else happening in the brain, besides computation. In a running computer, information about outside…
Ido Aizenbud, David Beniaguev, Noam Pnueli, Idan Segev + 1 more
Cortical pyramidal neurons possess elaborate dendritic trees with diverse nonlinear membrane conductances and thousands of plastic synapses, suggesting substantial computational capabilities at the single-cell level. Yet, what can a neuron compute remains an open question, largely due to the lack of a systematic…
Authors not listed
Data-driven strategies are reshaping computational materials design by accelerating the prediction of novel compounds with targeted functionalities. Beyond high-throughput screening, the integration of generative artificial intelligence enables exploration across vast chemical spaces comprising millions of known and…
Jingxian Fu, Anqiang Jia, Haiyang Wang, Hai-Jun Liu
The exponential growth of genomic data presents significant computational challenges for population genetics and genomic breeding. Here, we present JanusX, a unified and user-friendly platform integrating essential workflows for population genetics, including Genome-Wide Association Studies (GWAS) and Genomic Selection…
Giulio Ruffini, Ming Li
The regulator theorem states that, under certain conditions, any optimal controller must embody a model of the system it regulates, grounding the idea that controllers embed, explicitly or implicitly, internal models of the controlled. This principle underpins neuroscience and predictive brain theories like the…
Authors not listed
Computational chemistry has entered a new era where machine learning (ML) models—particularly graph neural networks and machine learning force fields—routinely deliver quantum mechanical accuracy at classical speeds, scaling to millions of atoms and reshaping workflows in drug discovery, catalysis, and materials…
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Chemistry curricula often separate “wet” experimental work from “dry” computation, yet modern discovery increasingly demands both. This Perspective offers an instructor-ready roadmap to train “hybrid chemists” within existing courses. We distill recent advances in machine learning, automation, and real-time analytics…
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The rapid growth of worldwide computing power has transformed in silico chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemi- cal processes at reasonable computational…
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Electrons have internal structure, you cannot have spin without internal structure, you cannot have chemistry without spin, computing with out an explicit model for spin has made chemists’ lives hard. We present a deterministic framework for computational chemistry that replaces the probabilistic wave function with a…
Remy Tuyeras, Alvaro Morcuende, Claudia Llinares, Asa Segerstolpe + 3 more
Functional specialization in continuous systems requires balancing adaptation to environmental stress with the preservation of encoded information. Yet, the physical constraints governing how living systems reconcile selective information retention with energetic structural reorganization remain unclear–a trade-off…
Authors not listed
Bridging AI and self-driving laboratories, we introduce the first fully-automated, closed-loop molecular discovery cycle, exemplified by the identification of novel JAK inhibitors. With minimal human intervention, we combined AI-driven molecular design and retrosynthesis with IBM’s synthesis automation system RoboRXN…