Tootfinder

Resonance Complexity Theory and the Architecture of Consciousness: A Field-Theoretic Model of Resonant Interference and Emergent Awareness
Michael Arnold Bruna
https://arxiv.org/abs/2505.20580

Resonance Complexity Theory and the Architecture of Consciousness: A Field-Theoretic Model of Resonant Interference and Emergent Awareness
This paper introduces Resonance Complexity Theory (RCT), which proposes that consciousness emerges from stable interference patterns of oscillatory neural activity. These patterns, shaped by recursive feedback and constructive interference, must exceed critical thresholds in complexity, coherence, gain, and fractal dimensionality to give rise to conscious experience. The resulting spatiotemporal attractors encode subjective awareness as dynamic resonance structures distributed across the neural…

The complexity of Ford domains of $\Gamma_0(N)$
Pengcheng Zhang
https://arxiv.org/abs/2508.18511 https://arxiv.org/pdf/2508.18511

The complexity of Ford domains of $Γ_0(N)$
For each integer $N>1$, we define a notion of complexity $c(N)$, which is a nonnegative integer and carries some information on the shape of the Ford fundamental domain of the congruence subgroup $Γ_0(N)$. The property that $c(N)=0$ first appeared as a technical assumption in a paper by Anke Pohl, which is closely related to a conjecture of Don Zagier on the "reduction theory" of $Γ_0(N)$. In this paper, we give a complete classification of integers $N>1$ with $c(N)=0$, and we also show that …

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/2]:
- Krylov complexity in quantum field theory, and beyond
Alexander Avdoshkin, Anatoly Dymarsky, Michael Smolkin

Control of Marine Robots in the Era of Data-Driven Intelligence
Lin Hong, Lu Liu, Zhouhua Peng, Fumin Zhang
https://arxiv.org/abs/2506.21063 https://

Control of Marine Robots in the Era of Data-Driven Intelligence
The control of marine robots has long relied on model-based methods grounded in classical and modern control theory. However, the nonlinearity and uncertainties inherent in robot dynamics, coupled with the complexity of marine environments, have revealed the limitations of conventional control methods. The rapid evolution of machine learning has opened new avenues for incorporating data-driven intelligence into control strategies, prompting a paradigm shift in the control of marine robots. This…

Replaced article(s) found for cs.GT. https://arxiv.org/list/cs.GT/new
[1/1]:
- The Complexity of Symmetric Bimatrix Games with Common Payoffs
Abheek Ghosh, Alexandros Hollender

On $NP \cap coNP$ proof complexity generators
Jan Krajicek
https://arxiv.org/abs/2506.20221 https://arxiv.org/pdf/2506.20221

On $NP \cap coNP$ proof complexity generators
Motivated by the theory of proof complexity generators we consider the following $Σ^p_2$ search problem $\mbox{DD}_P$ determined by a propositional proof system $P$: given a $P$-proof $π$ of a disjunction $\bigvee_i α_i$, no two $α_i$ having an atom in common, find $i$ such that $α_i \in \mbox{TAUT}$. We formulate a hypothesis (ST) that for some strong proof system $P$ the problem $\mbox{DD}_P$ is not solvable in the student-teacher model with a p-time student and a constant number of ro…

Edge Clique Partition and Cover Beyond Independence
Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, Kirill Simonov
https://arxiv.org/abs/2506.21216 https:…

Edge Clique Partition and Cover Beyond Independence
Covering and partitioning the edges of a graph into cliques are classical problems at the intersection of combinatorial optimization and graph theory, having been studied through a range of algorithmic and complexity-theoretic lenses. Despite the well-known fixed-parameter tractability of these problems when parameterized by the total number of cliques, such a parameterization often fails to be meaningful for sparse graphs. In many real-world instances, on the other hand, the minimum number of …

Tangling and Untangling Trees on Point-sets
Giuseppe Di Battista, Giuseppe Liotta, Maurizio Patrignani, Antonios Symvonis, Ioannis G. Tollis
https://arxiv.org/abs/2508.18535 htt…

Tangling and Untangling Trees on Point-sets
We study a question that lies at the intersection of classical research subjects in Topological Graph Theory and Graph Drawing: Computing a drawing of a graph with a prescribed number of crossings on a given set $S$ of points, while ensuring that its curve complexity (i.e., maximum number of bends per edge) is bounded by a constant. We focus on trees: Let $T$ be a tree, $\vartheta(T)$ be its thrackle number, and $χ$ be any integer in the interval $[0,\vartheta(T)]$. In the tangling phase we co…

Scaling the human niche
Marcus J. Hamilton
https://arxiv.org/abs/2506.20902 https://arxiv.org/pdf/2506.20902

Scaling the human niche
The human niche represents the intersection of biological, ecological, cultural, and technological processes that have co-evolved to shape human adaptation and societal complexity. This paper explores the human niche through the lens of macroecological scaling theory, seeking to define and quantify the dimensions along which human ecological strategies have diversified. By leveraging concepts from classic niche theory, niche construction, and complex adaptive systems, I develop a framework for …

Universal inverse Radon transforms: Complexity of Radon transforms and the hybrid functions
I. V. Anikin
https://arxiv.org/abs/2506.18911 https://

Universal inverse Radon transforms: Complexity of Radon transforms and the hybrid functions
For the reconstruction problem, the universal representation of inverse Radon transforms may imply the needed complexity of the direct Radon transforms which leads to the additional contributions. Meanwhile, in the standard theory of generalized functions, if the origin function which generates the Radon image is a pure-real function, as a rule the complexity of Radon transform becomes in question. In the letter, we demonstrate that the Fourier method together with the hybrid (Wigner-like) func…

from my link log —
RE#: high performance derivative-based regex matching with intersection, complement, and lookarounds.
https://arxiv.org/abs/2407.20479
saved 2025-04-17

RE#: High Performance Derivative-Based Regex Matching with Intersection, Complement and Lookarounds
We present a tool and theory RE# for regular expression matching that is built on symbolic derivatives, does not use backtracking, and, in addition to the classical operators, also supports complement, intersection and lookarounds. We develop the theory formally and show that the main matching algorithm has input-linear complexity both in theory as well as experimentally. We apply thorough evaluation on popular benchmarks that show that RE# is over 71% faster than the next fastest regex engine …

Pushing the Complexity Boundaries of Fixed-Point Equations: Adaptation to Contraction and Controlled Expansion
Jelena Diakonikolas
https://arxiv.org/abs/2506.17698

Pushing the Complexity Boundaries of Fixed-Point Equations: Adaptation to Contraction and Controlled Expansion
Fixed-point equations with Lipschitz operators have been studied for more than a century, and are central to problems in mathematical optimization, game theory, economics, and dynamical systems, among others. When the Lipschitz constant of the operator is larger than one (i.e., when the operator is expansive), it is well known that approximating fixed-point equations becomes computationally intractable even in basic finite-dimensional settings. In this work, we aim to push these complexity boun…

The Theory of Economic Complexity
C\'esar A. Hidalgo, Viktor Stojkoski
https://arxiv.org/abs/2506.18829 https://arxiv.org/pdf/250…

The Theory of Economic Complexity
Economic complexity estimates rely on eigenvectors derived from matrices of specialization to explain differences in economic growth, inequality, and sustainability. Yet, despite their widespread use, we still lack a principled theory that can deduce these eigenvectors from first principles and place them in the context of a mechanistic model. Here, we calculate these eigenvectors analytically for a model where the output of an economy in an activity increases with the probability the economy i…

Completions of Restricted Complexity I, Weak Arithmetical Theories
Ali Enayat, Mateusz {\L}e{\l}yk, Albert Visser
https://arxiv.org/abs/2508.14758 https://…

Completions of Restricted Complexity I, Weak Arithmetical Theories
Given a first-order theory $T$ formulated in the usual language of first-order arithmetic, we say that $T$ is of *restricted complexity* if there is some natural number $n$ and some set $\mathcal A$ of $Σ_n$-sentences such that $T$ can be axiomatized by $\mathcal A$. Motivated by the fact that no consistent arithmetical theory extending $\mathrm{I}Δ_{0}+\mathsf{Exp}$ has a consistent completion that is of restricted complexity, we construct models of arithmetic whose complete theories are of …

Time for another "review". This one's hard. While the book was quite interesting, it required me to be quite open-minded. Still, I think it's worth mentioning:
Robert Wright — Nonzero: The Logic of Human Destiny
The book basically focused on a thesis that both biological evolution and cultural evolution are a thing, they are directional and this directionality can be explained together using game theory — as eventually leading to more non-zero sum games.
It consists of three chapters. The first one is is focused on the history of civilization. It features many examples from different parts of the world, which makes it quite interesting. The author argues that the culture inevitably is evolving as information processing techniques improve — from writing to the Internet.
The second chapter is focused on biological evolution. Now, the argument is that it's not quite random, but actually directed towards greater complexity — eventually leading to the development of highly intelligent species, and a civilization.
The third chapter is quite speculative and metaphysical, and I'm just going to skip it.
The book is full of optimism. Capitalism creates freedom — because people are more productive when they're working for their own gain, so the free market eliminates slavery. Globalisation creates networks of interdependence that make wars uneconomic. Increased contacts between different cultures makes people more tolerant. And eventually, the humanity may be able to unite facing a common "external" enemy — the climate change.
What can I say? The examples are quite interesting, the whole theory seems self-consistent. Still, I repeatedly looked at the publication date (it's 1999), and wondered if author would write the same thing today (yes, I know I can search for his current opinions).
#books #bookstodon @…

A primer on the closure of algebraic complexity classes under factoring
C. S. Bhargav, Prateek Dwivedi, Nitin Saxena
https://arxiv.org/abs/2506.19604 https…

A primer on the closure of algebraic complexity classes under factoring
Polynomial factorization is a fundamental problem in computational algebra. Over the past half century, a variety of algorithmic techniques have been developed to tackle different variants of this problem. In parallel, algebraic complexity theory classifies polynomials into complexity classes based on their perceived `hardness'. This raises a natural question: Do these classes afford efficient factorization? In this survey, we revisit two pivotal techniques in polynomial factorization: Hensel…

An Algorithm Architecture for Radio Interferometric Data Processing
S. Bhatnagar, U. Rau, M. Hsieh, J. Kern, R. Xue
https://arxiv.org/abs/2508.17187 https://

An Algorithm Architecture for Radio Interferometric Data Processing
We present a foundational, scalable algorithm architecture for processing data from aperture synthesis radio telescopes. The analysis leading to the architecture is rooted in the theory of aperture synthesis, signal processing and numerical optimization keeping it scalable for variations in computing load, algorithmic complexity, and accommodate the continuing evolution of algorithms. It also adheres to scientific software design principles and use of modern performance engineering techniques p…

Replaced article(s) found for cs.FL. https://arxiv.org/list/cs.FL/new
[1/1]:
- The complexity of reachability problems in strongly connected finite automata
Stefan Kiefer, Andrew Ryzhikov

Complexity of sparse polynomial solving 3: Infinity
Gregorio Malajovich
https://arxiv.org/abs/2506.17086 https://arxiv.org/pdf/2506.1…

Complexity of sparse polynomial solving 3: Infinity
A theory of numerical path-following in toric varieties was suggested in two previous papers. The motivation is solving systems of polynomials with real or complex coefficients. When those polynomials are not assumed `dense', solving them over projective space or complex space may introduce spurious, degenerate roots or components.Spurious roots may be avoided by solving over toric varieties. In this paper, a homotopy algorithm is locally defined on charts of the toric variety. Its complexity…

Role of Non-conserved Gravity Theory and Electric Charge in Constructing Complexity-free Stellar Models: A Novel Approach under Non-minimal Coupling
Tayyab Naseer
https://arxiv.org/abs/2508.13903

Role of Non-conserved Gravity Theory and Electric Charge in Constructing Complexity-free Stellar Models: A Novel Approach under Non-minimal Coupling
This study explores the application of complexity factor within the context of Rastall gravity, exploring its implications on a static spacetime admitting spherical symmetry associated with anisotropic fluids under an electromagnetic field. The field equations are derived for a static charged sphere that provides a foundational framework for analyzing gravitational effects in this non-conserved theory. The mass function is formulated by incorporating both fluid and geometric parameters, offerin…

Lower Bounds for Conjunctive Query Evaluation
Stefan Mengel
https://arxiv.org/abs/2506.17702 https://arxiv.org/pdf/2506.17702

Lower Bounds for Conjunctive Query Evaluation
In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus will be on showing how different relatively recent hypotheses from complexity theory connect to query answering and allow showing that known algorithms in several cases can likely not be improved.

TRIZ Agents: A Multi-Agent LLM Approach for TRIZ-Based Innovation
Kamil Szczepanik, Jaros{\l}aw A. Chudziak
https://arxiv.org/abs/2506.18783 https://

TRIZ Agents: A Multi-Agent LLM Approach for TRIZ-Based Innovation
TRIZ, the Theory of Inventive Problem Solving, is a structured, knowledge-based framework for innovation and abstracting problems to find inventive solutions. However, its application is often limited by the complexity and deep interdisciplinary knowledge required. Advancements in Large Language Models (LLMs) have revealed new possibilities for automating parts of this process. While previous studies have explored single LLMs in TRIZ applications, this paper introduces a multi-agent approach. W…

Temporal Broadening of Attosecond Pulse Trains Induced by Multi-Band inference in Solid-State High-Order Harmonic Generation
Qing-Guo Fan, Kang Lai, Wen-hao Liu, Zhi Wang, Lin-Wang Wang, Jun-Wei Luo
https://arxiv.org/abs/2507.18019

Temporal Broadening of Attosecond Pulse Trains Induced by Multi-Band inference in Solid-State High-Order Harmonic Generation
The mechanism underlying high harmonic generation (HHG) in gases has been well clarified, characterizing attosecond pulse trains (APT) in the time domain, significantly advances the synthesis of isolated attosecond pulse (IAP). However, the complexity of HHG in solid obstacles IAP separation. Here, we use time-dependent density functional theory (TDDFT) to investigate the multiband mechanism of APT in solid state with bulk silicon as prototype. Our research unveils that: 1. The temporal charact…

Small Scale Index Theory, Scalar Curvature, and Gromov's Simplicial Norms
Qiaochu Ma, Guoliang Yu
https://arxiv.org/abs/2508.14791 https://arxiv.org/pd…

Small Scale Index Theory, Scalar Curvature, and Gromov's Simplicial Norms
In this article, we study the topological complexity of manifolds with a lower scalar curvature bound. We introduce a small-scale index theorem to establish an upper bound on Gromov's simplicial norm of the Poincaré dual of the $\hat{A}$-class for Riemannian manifolds satisfying a scalar curvature lower bound. This result can be considered as a topological finiteness theorem for manifolds with a lower scalar curvature bound.

A Brief Introduction to Quantum Query Complexity
Yassine Hamoudi
https://arxiv.org/abs/2508.08852 https://arxiv.org/pdf/2508.08852

A Brief Introduction to Quantum Query Complexity
Quantum query complexity is a fundamental model for analyzing the computational power of quantum algorithms. It has played a key role in characterizing quantum speedups, from early breakthroughs such as Grover's and Simon's algorithms to more recent developments in quantum cryptography and complexity theory. This document provides a structured introduction to quantum query lower bounds, focusing on four major techniques: the hybrid method, the polynomial method, the recording method, and the ad…

Stochastic stability of physical measures in conservative systems
Weiwei Qi, Zhongwei Shen, Yingfei Yi
https://arxiv.org/abs/2506.17598 https://

Stochastic stability of physical measures in conservative systems
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a fundamental issue in both theory and practice. The present paper is devoted to the stochastic stability of physical measures for conservative systems on a smooth, connected, and closed Riemannian manifold. It is assumed that a conservative system admits an …

On distributional one-category, diagonal distributional complexity, and related invariants
Ekansh Jauhari, John Oprea
https://arxiv.org/abs/2508.06973 https://

On distributional one-category, diagonal distributional complexity, and related invariants
We develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below. Unlike any other classical or probabilistic invariants, these invariants are rigid on spaces with finite fundamental group. On Eilenberg-Mac Lane spaces, we identify these new invariants with distributional category and complexity, respectively, and use them to illuminate aspects of the behavior of the latter invari…

Computability of Separation Axioms in Countable Second Countable Spaces
Andrew DeLapo, David Gonzalez
https://arxiv.org/abs/2507.18564 https://arxiv.org/pd…

Computability of Separation Axioms in Countable Second Countable Spaces
We analyze the effective content of countable, second countable topological spaces by directly calculating the complexity of several topologically defined index sets. We focus on the separation principles, calibrating an arithmetic completeness result for each of the Tychonoff separation axioms. Beyond this, we prove completeness results for various other topological properties, such as being Polish and having a particular Cantor-Bendixson rank, using tools from computable structure theory. Thi…

On the construction of a counterexample to Strassen's rank additivity conjecture
Viktoriia Borovik, Cosimo Flavi, Pawe{\l} Pielasa, Anatoli Shatsila, Jeyoung Song
https://arxiv.org/abs/2507.17890

On the construction of a counterexample to Strassen's rank additivity conjecture
The rank additivity conjecture, first formulated by Volker Strassen in 1973, states that the rank of the direct sum of two independent tensors is equal to the sum of their individual ranks. In the last decades, this conjecture has been a central topic in tensor rank theory and its implications for computational complexity. In 2019, Yaroslav Shitov disproved this conjecture in its general form by showing the existence of a counter-example using a dimension counting argument. In this paper, we pr…

Interesting stuff. This touches on a lot of work that was on my todo list. Especially estimating the "interestingness" of data by measuring the maximum compute needed to reach the optimal compression.
AIT is definitely becoming practically relevant.
https://arxiv.org/abs/2507.07995

Single-pass Adaptive Image Tokenization for Minimum Program Search
According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search o…

Total/dual correlation/coherence, redundancy/synergy, complexity, and O-information for real and complex valued multivariate data
Roberto D. Pascual-Marqui, Kieko Kochi, Toshihiko Kinoshita
https://arxiv.org/abs/2507.08773

Total/dual correlation/coherence, redundancy/synergy, complexity, and O-information for real and complex valued multivariate data
Firstly, assuming Gaussianity, equations for the following information theory measures are presented: total correlation/coherence (TC), dual total correlation/coherence (DTC), O-information, TSE complexity, and the redundancy-synergy index (RSI). Since these measures are functions of the covariance matrix "S" and its inverse "S^-1", the associated Wishart and inverse-Wishart distributions are of note. The DTC is shown here to be the Kullback-Leibler (KL) divergence for the inverse-Wishart pair …

Characterizing NC1 with Typed Monoids
Anuj Dawar, Aidan T. Evans
https://arxiv.org/abs/2508.11019 https://arxiv.org/pdf/2508.11019

Characterizing NC1 with Typed Monoids
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to infinite monoids and hence characterize classes beyond the regular languages. We advance this line of work beyond TC0 by giving a characterization of NC1. This is obtained by first showing that NC1 can be defined as the languages expressible in an extension of …

Orthogonal splitting of the Riemann curvature tensor and its implications in modeling compact stellar structures
A. Rehman, Tayyab Naseer, Nazek Alessa, Abdel-Haleem Abdel-Aty
https://arxiv.org/abs/2506.16725

Orthogonal splitting of the Riemann curvature tensor and its implications in modeling compact stellar structures
Although the interpretation of complexity in extended theories of gravity is available in the literature, its illustration in $f(R,L_{m},\mathcal{T})$ theory is still ambiguous. The orthogonal decomposition of the Riemann tensor results in the emergence of complexity factor as recently proposed by Herrera [1]. We initiate the analysis by contemplating the interior spacetime as a static spherical anisotropic composition under the presence of charge. The modified field equations are derived along…

How Complex is a Complex Network? Insights from Linear Systems Theory
Giacomo Baggio, Marco Fabris
https://arxiv.org/abs/2507.06389 https://

How Complex is a Complex Network? Insights from Linear Systems Theory
This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the effect of nodal dynamics in the interconnected system, we propose a new quantitative index of network complexity rooted in the notion of McMillan degree of a linear system. First, we show that network systems with the same interconnection structure share the s…

Single-pass Adaptive Image Tokenization for Minimum Program Search
Shivam Duggal, Sanghyun Byun, William T. Freeman, Antonio Torralba, Phillip Isola
https://arxiv.org/abs/2507.07995

Single-pass Adaptive Image Tokenization for Minimum Program Search
According to Algorithmic Information Theory (AIT) -- Intelligent representations compress data into the shortest possible program that can reconstruct its content, exhibiting low Kolmogorov Complexity (KC). In contrast, most visual representation learning systems use fixed-length representations for all inputs, ignoring variations in complexity or familiarity. Recent adaptive tokenization methods address this by allocating variable-length representations but typically require test-time search o…

Replaced article(s) found for cs.FL. https://arxiv.org/list/cs.FL/new
[1/1]:
- Fine-Grained Complexity of Ambiguity Problems on Automata and Directed Graphs
Karolina Drabik, Anita D\"urr, Fabian Frei, Filip Mazowiecki, Karol W\k{e}grzycki

Defining the Game Producer: A Mapping of Key Characteristics and Differentiators of the Professional Behind Digital Game Production
Rafael C. Lopes, Danilo M. Ribeiro
https://arxiv.org/abs/2506.14409

Defining the Game Producer: A Mapping of Key Characteristics and Differentiators of the Professional Behind Digital Game Production
Introduction: As digital games grow in complexity, the role of the Game Producer becomes increasingly relevant for aligning creative, technical, and business dimensions. Objective: This study aimed to identify and map the main characteristics, skills, and competencies that define the Digital Game Producer profile. Methodology: A qualitative investigation was conducted with 11 semi-structured interviews, analyzed through Grounded Theory to build categories grounded in professional practice. Resu…

Second-Order Parameterizations for the Complexity Theory of Integrable Functions
Aras Bacho, Martin Ziegler
https://arxiv.org/abs/2506.11210 https://

Second-Order Parameterizations for the Complexity Theory of Integrable Functions
We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized complexity theory for spaces of continuous functions. Specifically we prove the mutual linear equivalence of three natural parameterizations of the space $\Lrm{p}$ of $p$-integrable complex functions on the real unit interval: (binary) $\Lrm{p}$-modulus, rate of convergence of Fourier series, and rate of approximation by s…

Sampling Theory for Super-Resolution with Implicit Neural Representations
Mahrokh Najaf, Gregory Ongie
https://arxiv.org/abs/2506.09949 https://

Sampling Theory for Super-Resolution with Implicit Neural Representations
Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking spatial coordinates as inputs. However, unlike traditional pixel representations, little is known about the sample complexity of estimating images using INRs in the context of linear inverse problems. Towards this end, we study the sampling requirements for recove…

Properties of Egalitarian Sequences of Committees: Theory and Experiments
Paula B\"ohm, Robert Bredereck, Till Fluschnik
https://arxiv.org/abs/2508.14439 https://

Properties of Egalitarian Sequences of Committees: Theory and Experiments
We study the task of electing egalitarian sequences of $τ$ committees given a set of agents with additive utilities for candidates available on each of $τ$ levels. We introduce several rules for electing an egalitarian committee sequence as well as properties for such rules. We settle the computational complexity of finding a winning sequence for our rules and classify them against our properties. Additionally, we transform sequential election data from existing election data from the literat…

New Trends in Kinetic Theory Towards the Complexity of Living Systems
Nicola Bellomo, Diletta Burini, Jie Liao
https://arxiv.org/abs/2506.08752 https://

New Trends in Kinetic Theory Towards the Complexity of Living Systems
The development of a mathematics for living systems is one of the most challenging prospects of this century. The search began with the pioneering contribution of Ilia Prigogine, who developed methods from statistical physics to describe the dynamics of vehicular traffic. This visionary seminal research contribution has given rise to a great deal of research activity, which began at the end of the last century and has been further developed in this century by several authors who have developed …

This https://arxiv.org/abs/2408.05762 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDM_…

The complexity of computing the period and the exponent of a digraph
The period of a strongly connected digraph is the greatest common divisor of the lengths of all its cycles. The period of a digraph is the least common multiple of the periods of its strongly connected components. These notions play an important role in the theory of Markov chains and the analysis of powers of nonnegative matrices. While the time complexity of computing the period is well-understood, little is known about its space complexity. We show that the problem of computing the period of…

Replaced article(s) found for cs.IT. https://arxiv.org/list/cs.IT/new
[1/1]:
- PAC codes with Bounded-Complexity Sequential Decoding: Pareto Distribution and Code Design
Mohsen Moradi, Hessam Mahdavifar

Impact of electronic correlations on the superconductivity of high-pressure CeH9
Siyu Chen, Yao Wei, Bartomeu Monserrat, Jan M. Tomczak, Samuel Ponc\'e
https://arxiv.org/abs/2507.12506

Impact of electronic correlations on the superconductivity of high-pressure CeH9
Rare-earth superhydrides have attracted considerable attention because of their high critical superconducting temperature under extreme pressures. They are known to have localized valence electrons, implying strong electronic correlations. However, such many-body effects are rarely included in first-principles studies of rare-earth superhydrides because of the complexity of their high-pressure phases. In this work, we use a combined density functional theory and dynamical mean-field theory appr…

Siamese Neural Network for Label-Efficient Critical Phenomena Prediction in 3D Percolation Models
Shanshan Wang, Dian Xu, Jianmin Shen, Feng Gao, Wei Li, Weibing Deng
https://arxiv.org/abs/2507.14159

Siamese Neural Network for Label-Efficient Critical Phenomena Prediction in 3D Percolation Models
Percolation theory serves as a cornerstone for studying phase transitions and critical phenomena, with broad implications in statistical physics, materials science, and complex networks. However, most machine learning frameworks for percolation analysis have focused on two-dimensional systems, oversimplifying the spatial correlations and morphological complexity of real-world three-dimensional materials. To bridge this gap and improve label efficiency and scalability in 3D systems, we propose a…

This https://arxiv.org/abs/2311.18804 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Holographic complexity of the Klebanov-Strassler background
We study the complexity of the gravity dual to the confining $SU(N)\times SU(N+M)$ Klebanov-Strassler gauge theory, which is an important test case for holographic complexity in higher-dimensional and nonconformal gauge/gravity dualities. We emphasize the dependence of the complexity on parameters of the gauge theory, finding a common behavior with confinement scale for several complexity functionals. We also analyze how the complexity diverges with the UV cut off, which is more complicated tha…

Verification Cost Asymmetry in Cognitive Warfare: A Complexity-Theoretic Framework
Joshua Luberisse
https://arxiv.org/abs/2507.21258 https://arxiv.org/pdf/…

Verification Cost Asymmetry in Cognitive Warfare: A Complexity-Theoretic Framework
Human verification under adversarial information flow operates as a cost-bounded decision procedure constrained by working memory limits and cognitive biases. We introduce the Verification Cost Asymmetry (VCA) coefficient, formalizing it as the ratio of expected verification work between populations under identical claim distributions. Drawing on probabilistically checkable proofs (PCP) and parameterized complexity theory, we construct dissemination protocols that reduce verification for truste…

Cognitive Load and Information Processing in Financial Markets: Theory and Evidence from Disclosure Complexity
Yimin Du, Guolin Tang
https://arxiv.org/abs/2507.07037 https://

Cognitive Load and Information Processing in Financial Markets: Theory and Evidence from Disclosure Complexity
We develop a theoretical framework for understanding how cognitive load affects information processing in financial markets and test it using exogenous variation in disclosure complexity. Our model distinguishes between attention allocation and cognitive processing capacity, showing that complex information creates differential effects across investor types. Using a comprehensive dataset of corporate disclosures and a novel identification strategy based on regulatory changes, we find that cogni…

Using Dynamical Systems Theory to Quantify Complexity in Asymptotic Lenia
Ivan Yevenko, Hiroki Kojima, Chrystopher L. Nehaniv
https://arxiv.org/abs/2508.02935 https://

Using Dynamical Systems Theory to Quantify Complexity in Asymptotic Lenia
Continuous cellular automata (CCAs) have evolved from discrete lookup tables to continuous partial differential equation (PDE) formulations in the search for novel forms of complexity. Despite innovations in qualitative behavior, analytical methods have lagged behind, reinforcing the notion that emergent complexity defies simple explanation. In this paper, we demonstrate that the PDE formulation of Asymptotic Lenia enables rigorous analysis using dynamical systems theory. We apply the concepts …

The Complexity of the Set of Validities of a Theory
Denis Hirschfeldt, Henry Towsner, Scott Weinstein
https://arxiv.org/abs/2506.08901 https://

The Complexity of the Set of Validities of a Theory
We study the collection of first-order logical schemata all of whose instances are theorems of a given theory $T$; we call these the validities of $T$ ($\mathsf{V}(T)$). It is easy to see that if $T$ is a decidable theory, then $\mathsf{V}(T)$ is distinct from the set of valid formulas of first-order logic as customarily understood. We provide a complete model-theoretic characterization of the complexity, in the sense of Turing degree, of $\mathsf{V}(T)$ for decidable theories $T$, and answer a…

On zeros and algorithms for disordered systems: mean-field spin glasses
Ferenc Bencs, Kuikui Liu, Guus Regts
https://arxiv.org/abs/2507.15616 https://

On zeros and algorithms for disordered systems: mean-field spin glasses
Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design deterministic quasipolynomial-time algorithms for estimating the partition function to arbitrarily high accuracy for nearly all inverse temperatures in the second moment regime. In particular, for the Sherrington--Kirkpatrick model, our algorithms succeed for almost …

The unreasonable likelihood of being: origin of life, terraforming, and AI
Robert G. Endres
https://arxiv.org/abs/2507.18545 https://arxiv.org/pdf/2507.185…

The unreasonable likelihood of being: origin of life, terraforming, and AI
The origin of life on Earth via the spontaneous emergence of a protocell prior to Darwinian evolution remains a fundamental open question in physics and chemistry. Here, we develop a conceptual framework based on information theory and algorithmic complexity. Using estimates grounded in modern computational models, we evaluate the difficulty of assembling structured biological information under plausible prebiotic conditions. Our results highlight the formidable entropic and informational barri…

${\sf QMA}={\sf QMA}_1$ with an infinite counter
Stacey Jeffery, Freek Witteveen
https://arxiv.org/abs/2506.15551 https://arxiv.org/p…

${\sf QMA}={\sf QMA}_1$ with an infinite counter
A long-standing open problem in quantum complexity theory is whether ${\sf QMA}$, the quantum analogue of ${\sf NP}$, is equal to ${\sf QMA}_1$, its one-sided error variant. We show that ${\sf QMA}={\sf QMA}^{\infty}= {\sf QMA}_1^{\infty}$, where ${\sf QMA}_1^\infty$ is like ${\sf QMA}_1$, but the verifier has an infinite register, as part of their witness system, in which they can efficiently perform a shift (increment) operation. We call this register an ``infinite counter'', and compare it t…

Recognizing Penny and Marble Graphs is Hard for Existential Theory of the Reals
Anna Lubiw, Marcus Schaefer
https://arxiv.org/abs/2508.10136 https://arxiv.…

Recognizing Penny and Marble Graphs is Hard for Existential Theory of the Reals
We show that the recognition problem for penny graphs (contact graphs of unit disks in the plane) is $\exists\mathbb{R}$-complete, that is, computationally as hard as the existential theory of the reals, even if a combinatorial plane embedding of the graph is given. The exact complexity of the penny graph recognition problem has been a long-standing open problem. We lift the penny graph result to three dimensions and show that the recognition problem for marble graphs (contact graphs of unit …

Presburger Functional Synthesis: Complexity and Tractable Normal Forms
S. Akshay, A. R. Balasubramanian, Supratik Chakraborty, Georg Zetzsche
https://arxiv.org/abs/2508.07207 ht…

Presburger Functional Synthesis: Complexity and Tractable Normal Forms
Given a relational specification between inputs and outputs as a logic formula, the problem of functional synthesis is to automatically synthesize a function from inputs to outputs satisfying the relation. Recently, a rich line of work has emerged tackling this problem for specifications in different theories, from Boolean to general first-order logic. In this paper, we launch an investigation of this problem for the theory of Presburger Arithmetic, that we call Presburger Functional Synthesis …

Exploring Quantum Heider Balance Theory
Anahid Kiani, S. Mahdi Fazeli, G. Reza Jafari
https://arxiv.org/abs/2507.00238 https://arxiv.…

Exploring Quantum Heider Balance Theory
Classical Heider balance theory models the evolution of social networks towards balanced states with stress minimization. Triad relationships are classically either balanced or imbalanced. However, real-world relationships often exhibit uncertainty, complexity, and interconnected dynamics that transcend this classical framework, and we will sometimes see the synchronicity of balance and imbalance states. When these triadics are simultaneously balanced and imbalanced, they form superposition and…

Descriptive set theory of separable Fr\'echet spaces
Bruno de Mendon\c{c}a Braga, Willian Hans Goes Corr\^ea, Valentin Ferenczi
https://arxiv.org/abs/2508.09368 https://

Descriptive set theory of separable Fréchet spaces
In the past few decades, much has been done regarding the descriptive set theory of separable Banach spaces. However, the descriptive properties of separable Fréchet spaces have not yet been investigated. In these notes, we look at this problem, its relation with the (now standard) theory for separable Banach spaces, and we compute/estimate the descriptive complexity of some classical classes of separable Fréchet spaces such as Fréchet-Hilbert, Schwartz, nuclear, and Montel spaces. Our main …

From Theory to Practice: Advancing Multi-Robot Path Planning Algorithms and Applications
Teng Guo
https://arxiv.org/abs/2506.09914 https://

From Theory to Practice: Advancing Multi-Robot Path Planning Algorithms and Applications
The labeled MRPP (Multi-Robot Path Planning) problem involves routing robots from start to goal configurations efficiently while avoiding collisions. Despite progress in solution quality and runtime, its complexity and industrial relevance continue to drive research. This dissertation introduces scalable MRPP methods with provable guarantees and practical heuristics. First, we study dense MRPP on 2D grids, relevant to warehouse and parcel systems. We propose the Rubik Table method, achieving …

The self is not singular but a fluid network of identities | Aeon Essays https://aeon.co/essays/the-self-is-not-singular-but-a-fluid-network-of-identities

The self is not singular but a fluid network of identities | Aeon Essays
You cannot be reduced to a body, a mind or a particular social role. An emerging theory of selfhood gets this complexity

Leveraging active learning-enhanced machine-learned interatomic potential for efficient infrared spectra prediction
Nitik Bhatia, Patrick Rinke, Ondrej Krejci
https://arxiv.org/abs/2506.13486

Leveraging active learning-enhanced machine-learned interatomic potential for efficient infrared spectra prediction
Infrared (IR) spectroscopy is a pivotal analytical tool as it provides real-time molecular insight into material structures and enables the observation of reaction intermediates in situ. However, interpreting IR spectra often requires high-fidelity simulations, such as density functional theory based ab-initio molecular dynamics, which are computationally expensive and therefore limited in the tractable system size and complexity. In this work, we present a novel active learning-based framework…

This https://arxiv.org/abs/1908.09164 has been replaced.
link: https://scholar.google.com/scholar?q=a

A homological approach to chromatic complexity of algebraic K-theory
The family of Thom spectra $y(n)$ interpolates between the sphere spectrum and the mod two Eilenberg--MacLane spectrum. Computations of Mahowald, Ravenel, Shick, and the authors show that the associative ring spectrum $y(n)$ has type $n$. Using trace methods, we give evidence that algebraic K-theory preserves this chromatic complexity. Our approach sheds light on the chromatic complexity of topological negative cyclic homology and topological periodic cyclic homology, which approximate algebrai…

This https://arxiv.org/abs/2401.16983 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Classification complexity of chaotic systems
In this paper, we deal with the classification complexity of continuous (Devaney) chaotic systems in dimensions $0,1$ and $\infty$ using the framework of invariant descriptive set theory. We identify the complexity in dimensions $0$ and $\infty$, while in dimension $1$ we get some partial results. More precisely, we prove the topological conjugacy relation of invertible chaotic systems on the Hilbert cube (resp. on all compact metric spaces) has the same complexity as (i.e. is Borel bireducib…

Interpolation in Classical Propositional Logic
Patrick Koopmann, Christoph Wernhard, Frank Wolter
https://arxiv.org/abs/2508.11449 https://arxiv.org/pdf/25…

Interpolation in Classical Propositional Logic
We introduce Craig interpolation and related notions such as uniform interpolation, Beth definability, and theory decomposition in classical propositional logic. We present four approaches to computing interpolants: via quantifier elimination, from formulas in disjunctive normal form, and by extraction from resolution or tableau refutations. We close with a discussion of the size of interpolants and links to circuit complexity.

On the Complexity of the Optimal Correlated Equilibria in Extensive-Form Games
Vincent Cheval, Florian Horn, Soumyajit Paul, Mahsa Shirmohammadi
https://arxiv.org/abs/2507.11509

On the Complexity of the Optimal Correlated Equilibria in Extensive-Form Games
A major open question in algorithmic game theory is whether normal-form correlated equilibria (NFCE) can be computed efficiently in succinct games such as extensive-form games [DFF+25,6PR24,FP23,HvS08,VSF08,PR08]. Motivated by this question, we study the associated Threshold problem: deciding whether there exists a correlated equilibrium whose value exceeds a given threshold. We prove that this problem is PSPACE-hard for NFCE in multiplayer extensive-form games with perfect recall, even for fix…

Reduced Order Data-driven Twin Models for Nonlinear PDEs by Randomized Koopman Orthogonal Decomposition and Explainable Deep Learning
D. A. Bistrian
https://arxiv.org/abs/2508.03325

Reduced Order Data-driven Twin Models for Nonlinear PDEs by Randomized Koopman Orthogonal Decomposition and Explainable Deep Learning
This study introduces a data-driven twin modeling framework based on modern Koopman operator theory, offering a significant advancement over classical modal decomposition by accurately capturing nonlinear dynamics with reduced complexity and no manual parameter adjustment. The method integrates a novel algorithm with Pareto front analysis to construct a compact, high-fidelity reduced-order model that balances accuracy and efficiency. An explainable NLARX deep learning framework enables real-tim…

A Dopamine-Serotonin Theory of Consciousness
Diogo Sousa
https://arxiv.org/abs/2507.02614 https://arxiv.org/pdf/2507.02614

A Dopamine-Serotonin Theory of Consciousness
This work presents a comprehensive theory of consciousness grounded in mathematical formalism and supported by clinical data analysis. The framework developed herein demonstrates that consciousness exists as a continuous, non-monotonic function across a high-dimensional neurochemical space, with dopamine serving as the primary intensity regulator and serotonin (5-HT2A) as the complexity modulator. This work offers mechanistic explanations for the full spectrum of conscious states, from deep sle…

CFT Complexity and Penalty Factors
Stefano Baiguera, Nicolas Chagnet, Shira Chapman, Osher Shoval
https://arxiv.org/abs/2507.22118 https://arxiv.org/pdf/25…

CFT Complexity and Penalty Factors
Quantum complexity of conformal field theory (CFT) states has recently gained significant attention, both as a diagnostic tool in condensed matter systems and in connection with holographic observables probing black hole interiors. Previous studies have primarily focused on cases where all generators of the conformal group contribute equally to the cost of building a circuit. In this work, we present a general framework for studying the complexity of circuits in generic Lie groups, where penalt…

Towards Bridging Formal Methods and Human Interpretability
Abhijit Paul, Proma Chowdhury, Kazi Sakib
https://arxiv.org/abs/2506.09759 https://

Towards Bridging Formal Methods and Human Interpretability
Labeled Transition Systems (LTS) are integral to model checking and design repair tools. System engineers frequently examine LTS designs during model checking or design repair to debug, identify inconsistencies, and validate system behavior. Despite LTS's significance, no prior research has examined human comprehension of these designs. To address this, we draw on traditional software engineering and graph theory, identifying 7 key metrics: cyclomatic complexity, state space size, average branc…

Back to Bits: Extending Shannon's communication performance framework to computing
Max Hawkins, Richard Vuduc
https://arxiv.org/abs/2508.05621 https://…

Back to Bits: Extending Shannon's communication performance framework to computing
This work proposes a novel computing performance unit grounded in information theory. Modern computing systems are increasingly diverse, supporting low-precision formats, hardware specialization, and emerging paradigms such as analog, quantum, and reversible logic. Traditional metrics like floating-point operations (flops) no longer accurately capture this complexity. We frame computing as the transformation of information through a channel and define performance in terms of the mutual informat…

The Complexity of Thermalization in Finite Quantum Systems
Dhruv Devulapalli, T. C. Mooney, James D. Watson
https://arxiv.org/abs/2507.00405 https://

The Complexity of Thermalization in Finite Quantum Systems
Thermalization is the process through which a physical system evolves toward a state of thermal equilibrium. Determining whether or not a physical system will thermalize from an initial state has been a key question in condensed matter physics. Closely related questions are determining whether observables in these systems relax to stationary values, and what those values are. Using tools from computational complexity theory, we demonstrate that given a Hamiltonian on a finite-sized system, dete…

Mapping correlations and coherence: adjacency-based approach to data visualization and regularity discovery
Guang-Xing Li
https://arxiv.org/abs/2506.05758 …

Mapping correlations and coherence: adjacency-based approach to data visualization and regularity discovery
The development of science has been transforming man's view towards nature for centuries. Observing structures and patterns in an effective approach to discover regularities from data is a key step toward theory-building. With increasingly complex data being obtained, revealing regularities systematically has become a challenge. Correlation is a most commonly-used and effective approach to describe regularities in data, yet for complex patterns, spatial inhomogeneity and complexity can often un…

VC-dimension of generalized progressions in some nonabelian groups
Gabriel Conant, Aycin Iplikci Arodirik, Tora Ozawa, David Zeng
https://arxiv.org/abs/2505.21789

VC-dimension of generalized progressions in some nonabelian groups
We analyze generalized progressions in some nonabelian groups using a measure of complexity called VC-dimension, which was originally introduced in statistical learning theory by Vapnik and Chervonenkis. Here by a "generalized progression" in a group $G$, we mean a finite subset of $G$ built from a fixed set of generators in analogy to a (multidimensional) arithmetic progression of integers. These sets play an important role in additive combinatorics and, in particular, the study of approximate…

Beyond Scalars: Zonotope-Valued Utility for Representation of Multidimensional Incomplete Preferences
Behrooz Moosavi Ramezanzadeh
https://arxiv.org/abs/2507.05844

Beyond Scalars: Zonotope-Valued Utility for Representation of Multidimensional Incomplete Preferences
In this paper, I propose a new framework for representing multidimensional incomplete preferences through zonotope-valued utilities, addressing the shortcomings of traditional scalar and vector-based models in decision theory. Traditional approaches assign single numerical values to alternatives, failing to capture the complexity of preferences where alternatives remainmain incomparable due to conflicting criteria across multiple dimensions. Our method maps each alternative to a zonotope, a con…

A parallel algorithm for the computation of the Jones polynomial
Kasturi Barkataki, Eleni Panagiotou
https://arxiv.org/abs/2505.23101 https://

A parallel algorithm for the computation of the Jones polynomial
Knots, links and entangled filaments appear in many physical systems of interest in biology and engineering. Classifying knots and measuring entanglement is of interest both for advancing knot theory, as well as for analyzing large data that become available through experiments or Artificial Intelligence. In this context, the efficient computation of topological invariants and other metrics of entanglement becomes an urgent issue. The computation of common measures of topological complexity, su…

Stark-Coleman Invariants and Quantum Lower Bounds: An Integrated Framework for Real Quadratic Fields
Ruopengyu Xu, Chenglian Liu
https://arxiv.org/abs/2506.07640

Stark-Coleman Invariants and Quantum Lower Bounds: An Integrated Framework for Real Quadratic Fields
Class groups of real quadratic fields represent fundamental structures in algebraic number theory with significant computational implications. While Stark's conjecture establishes theoretical connections between special units and class group structures, explicit constructions have remained elusive, and precise quantum complexity bounds for class group computations are lacking. Here we establish an integrated framework defining Stark-Coleman invariants $κ_p(K) = \log_p \left( \frac{\varepsilon_…

MichelangeRoll: Sculpting Rational Distributions Exactly and Efficiently
Jui-Hsiang Shao, Hsin-Po Wang
https://arxiv.org/abs/2507.00915 https://

MichelangeRoll: Sculpting Rational Distributions Exactly and Efficiently
Simulating an arbitrary discrete distribution $D \in [0, 1]^n$ using fair coin tosses incurs trade-offs between entropy complexity and space and time complexity. Shannon's theory suggests that $H(D)$ tosses are necessary and sufficient, but does not guarantee exact distribution. Knuth and Yao showed that a decision tree consumes fewer than $H(D) + 2$ tosses for one exact sample. Drapper and Saad's recent work addresses the space and time aspect, showing that $H(D) + 2$ tosses, $O(n \log(n) \log…

Study of Complexity Factor and Stability of Dynamical Systems in $f(G)$ Gravity
M. Zeeshan Gul, W. Ahmad, M. M. M. Nasir, Faisal Javed, Orhan Donmez, Bander Almutairi
https://arxiv.org/abs/2506.03559

Study of Complexity Factor and Stability of Dynamical Systems in $f(G)$ Gravity
In this paper, we evaluate the complexity of the non-static cylindrical geometry with anisotropic matter configuration in the framework of modified Gauss-Bonnet theory. In this perspective, we calculate modified field equations, the C energy formula, and the mass function that helps to understand the astrophysical structures in this modified gravity. Furthermore, we use the Weyl tensor and obtain different structure scalars by orthogonally splitting the Riemann tensor. One of these scalars, $YT…

A Conceptual Introduction to Hetero-functional Graph Theory for Systems-of-Systems
Amro M. Farid, Amirreza Hosseini, John C. Little
https://arxiv.org/abs/2505.24046

A Conceptual Introduction to Hetero-functional Graph Theory for Systems-of-Systems
A defining feature of twenty first century engineering challenges is their inherent complexity, demanding the convergence of knowledge across diverse disciplines. Establishing consistent methodological foundations for engineering systems remains a challenge -- one that both systems engineering and network science have sought to address. Model-based systems engineering (MBSE) has recently emerged as a practical, interdisciplinary approach for developing complex systems from concept through imple…

Computational complexity of covering regular trees
Jan Bok, Ji\v{r}\'i Fiala, Nikola Jedli\v{c}kov\'a, Jan Kratochv\'il
https://arxiv.org/abs/2507.00564

Computational complexity of covering regular trees
A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph theory but has also found applications in combinatorics and theoretical computer science. In this paper we consider undirected graphs in the most general setting -- graphs may contain multiple edges, loops, and semi-edges. This is in line with recent trends in …

Reshaping the anomalous Hall response in tilted 3D system with disorder correction
Vivek Pandey, Pankaj Bhalla
https://arxiv.org/abs/2507.00744 https://

Reshaping the anomalous Hall response in tilted 3D system with disorder correction
The anomalous Hall conductivity in the nodal line semimetals (NLSMs) due to the presence of a symmetry-protected nodal ring adds complexity in the investigation of their transport properties. By employing quantum kinetic theory and considering the weak disorder limit, we analyze the intraband and interband parts of anomalous Hall conductivity in the tilted 3D Dirac NLSMs. Our findings reveal that the net anomalous response is mainly contributed by the interband part. Further, the latter part gi…

FPT Parameterisations of Fractional and Generalised Hypertree Width
Matthias Lanzinger, Igor Razgon, Daniel Unterberger
https://arxiv.org/abs/2507.11080 ht…

FPT Parameterisations of Fractional and Generalised Hypertree Width
We present the first fixed-parameter tractable (fpt) algorithms for precisely determining several central hypergraph decomposition parameters, including generalized hypertree width, fractional hypertree width, and adaptive width. Despite the recognized importance of these measures in complexity theory, databases, and constraint satisfaction, no exact fpt algorithms for any of them had previously been known. Our results are obtained for hypergraph classes of bounded rank and bounded degree. Ou…

Extensional Independence
Taishi Kurahashi, Albert Visser
https://arxiv.org/abs/2506.13524 https://arxiv.org/pdf/2506.13524

Extensional Independence
Joel Hamkins asks whether there is a $Π^0_1$-formula $ρ(x)$ such that $ρ(ϕ)$ is independent over ${\sf PA}+ϕ$, if this theory is consistent, where this construction is extensional in $ϕ$ with respect to {\sf PA}-provable equivalence. We show that there can be no such extensional Rosser formula of any complexity. We give a positive answer to Hamkins' question for the case where we replace Extensionality by a weaker demand \emph{Consistent Extensionality}. We also prove that we can demand…

From macro to micro: Economic complexity indicators for firm growth
Valerio De Stefano, Maddalena Mula, Manuel Sebastian Mariani, Andrea Zaccaria
https://arxiv.org/abs/2507.21754

From macro to micro: Economic complexity indicators for firm growth
A rich theoretical and empirical literature investigated the link between export diversification and firm performance. Prior theoretical works hinted at the key role of capability accumulation in shaping production activities and performance, without however producing product-level indicators able to forecast corporate growth. Building on economic complexity theory and the corporate growth literature, this paper examines which characteristics of a firm's export basket predict future performance…

Replaced article(s) found for cs.FL. https://arxiv.org/list/cs.FL/new
[1/1]:
- The Complexity of Pure Strategy Relevant Equilibria in Concurrent Games
Purandar Bhaduri

Krylov exponents and power spectra for maximal quantum chaos: an EFT approach
Saskia Demulder, Maria Knysh, Andrew Rolph
https://arxiv.org/abs/2508.05444 https://

Krylov exponents and power spectra for maximal quantum chaos: an EFT approach
We examine the effective field theory (EFT) of maximal chaos through the lens of Krylov complexity and the Universal Operator Growth Hypothesis. We test the relationship between two measures of quantum chaos: out-of-time-ordered correlators (OTOCs) and Krylov complexity. In the EFT, a shift symmetry of the hydrodynamic modes enforces the maximal Lyapunov exponent in OTOCs, $λ_L = 2πT$, while simultaneously constraining thermal two-point autocorrelators. We solve these constraints on the autoc…

Coordinate-independent model reductions of chemical reaction networks based on geometric singular perturbation theory
Timothy Earl Figueroa Lapuz, Martin Wechselberger
https://arxiv.org/abs/2508.03304 …

Coordinate-independent model reductions of chemical reaction networks based on geometric singular perturbation theory
The quasi-steady-state approximation (QSSA) is a standard technique for reducing the complexity of chemical reaction networks (CRNs). The validity of any QSSA-based model is restricted to specific parameter regimes, which often overlap, meaning multiple different reduced models can be simultaneously valid. This ambiguity complicates unnecessarily the analysis, as selecting the appropriate reduction is not always straightforward. Here, we employ a more powerful alternative: coordinate-independ…

Information-Optimal Sensing and Control in High-Intensity Laser Experiments
A. D\"opp, C. Eberle, J. Esslinger, S. Howard, F. Irshad, J. Schroeder, N. Weisse, S. Karsch
https://arxiv.org/abs/2506.04946

Information-Optimal Sensing and Control in High-Intensity Laser Experiments
High-intensity laser systems present unique measurement and optimization challenges due to their high complexity, low repetition rates, and shot-to-shot variations. We discuss recent developments towards a unified framework based on information theory and Bayesian inference that addresses these challenges. Starting from fundamental constraints on the physical field structure, we recently demonstrated how to capture complete spatio-temporal information about individual petawatt laser pulses. Bui…

The Complexity of Correlated Equilibria in Generalized Games
Martino Bernasconi, Matteo Castiglioni, Andrea Celli, Gabriele Farina
https://arxiv.org/abs/2506.01899

The Complexity of Correlated Equilibria in Generalized Games
Correlated equilibria -- and their generalization $Φ$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of equilibrium computation are well-understood in some settings, fundamental questions are still open in generalized games, that is, games in which the set of strategies allowed to each player depends on the other players' strategies. These classes of games model funda…

Finding One Local Optimum Is Easy -- But What about Two?
Yasuaki Kobayashi, Kazuhiro Kurita, Yutaro Yamaguchi
https://arxiv.org/abs/2507.07524 https://

Finding One Local Optimum Is Easy -- But What about Two?
The class PLS (Polynomial Local Search) captures the complexity of finding a solution that is locally optimal and has proven to be an important concept in the theory of local search. It has been shown that local search versions of various combinatorial optimization problems, such as Maximum Independent Set and Max Cut, are complete for this class. Such computational intractability typically arises in local search problems allowing arbitrary weights; in contrast, for unweighted problems, locally…

Entropy measures as indicators of connectivity paths in the human brain
Ania Mesa-Rodr\'iguez, Ernesto Estevez-Rams, Holger Kantz
https://arxiv.org/abs/2507.04442

Entropy measures as indicators of connectivity paths in the human brain
How does the information flow between different brain regions during various stimuli? This is the question we aim to address by studying complex cognitive paradigms in terms of Information Theory. To assess creativity and the emergence of patterns from a Shannon perspective, we applied a range of tools, including Entropy Density, Effective Measure Complexity, and the Lempel-Ziv distance. These entropic tools enable the detection of both linear and non-linear dynamics without relying on pre-esta…

A Formal Refutation of the Blockchain Trilemma
Craig Wright
https://arxiv.org/abs/2507.05809 https://arxiv.org/pdf/2507.05809

A Formal Refutation of the Blockchain Trilemma
The so-called blockchain trilemma asserts the impossibility of simultaneously achieving scalability, security, and decentralisation within a single blockchain protocol. In this paper, we formally refute that proposition. Employing predicate logic, formal automata theory, computational complexity analysis, and graph-theoretic measures of relay topology--specifically Baran's model of network path redundancy--we demonstrate that the trilemma constitutes a category error, conflates distinct analyti…

Replaced article(s) found for cs.GT. https://arxiv.org/list/cs.GT/new
[1/1]:
- The Complexity of Pure Strategy Relevant Equilibria in Concurrent Games
Purandar Bhaduri

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/2]:
- Krylov Complexity as a Probe for Chaos
Mohsen Alishahiha, Souvik Banerjee, Mohammad Javad Vasli

A multi-parameter expansion for the evolution of asymmetric binaries in astrophysical environments
Sayak Datta, Andrea Maselli
https://arxiv.org/abs/2507.04471

A multi-parameter expansion for the evolution of asymmetric binaries in astrophysical environments
Compact binaries with large mass asymmetries - such as Extreme and Intermediate Mass Ratio Inspirals - are unique probes of the astrophysical environments in which they evolve. Their long-lived and intricate dynamics allow for precise inference of source properties, provided waveform models are accurate enough to capture the full complexity of their orbital evolution. In this work, we develop a multi-parameter formalism, inspired by vacuum perturbation theory, to model asymmetric binaries embed…

Replaced article(s) found for econ.GN. https://arxiv.org/list/econ.GN/new
[1/1]:
- The Theory of Economic Complexity
C\'esar A. Hidalgo, Viktor Stojkoski
ht…

On integrable structure of the null string in (anti-)de Sitter space
D. V. Uvarov
https://arxiv.org/abs/2508.04158 https://arxiv.org/pdf/2508.04158

On integrable structure of the null string in (anti-)de Sitter space
Presently integrability turned the key property in the study of duality between superconformal gauge theories and strings in anti-de Sitter superspaces. Complexity of the study of integrable structure in string theory is caused by complicated dependence of background fields of the Type II supergravity multiplets, with which strings interact, on the superspace coordinates. This explains an interest to study of limiting cases, in which superstring equations simplify. In the present work considere…

Replaced article(s) found for cs.GT. https://arxiv.org/list/cs.GT/new
[1/1]:
- Logarithmic Comparison-Based Query Complexity for Fair Division of Indivisible Goods
Xiaolin Bu, Zihao Li, Shengxin Liu, Jiaxin Song, Biaoshuai Tao

Learning DNF through Generalized Fourier Representations
Mohsen Heidari, Roni Khardon
https://arxiv.org/abs/2506.01075 https://arxiv.…

Learning DNF through Generalized Fourier Representations
The Fourier representation for the uniform distribution over the Boolean cube has found numerous applications in algorithms and complexity analysis. Notably, in learning theory, learnability of Disjunctive Normal Form (DNF) under uniform as well as product distributions has been established through such representations. This paper makes five main contributions. First, it introduces a generalized Fourier expansion that can be used with any distribution $D$ through the representation of the distr…

This https://arxiv.org/abs/2211.07055 has been replaced.
link: https://scholar.google.com/scholar?q=a

Geometric complexity theory for product-plus-power
According to Kumar's recent surprising result (ToCT'20), a small border Waring rank implies that the polynomial can be approximated as a sum of a constant and a small product of linear polynomials. We prove the converse of Kumar's result and establish a tight connection between border Waring rank and the model of computation in Kumar's result. In this way, we obtain a new formulation of border Waring rank, up to a factor of the degree. We connect this new formulation to the orbit closure proble…

Pseudo-Equilibria, or: How to Stop Worrying About Crypto and Just Analyze the Game
Alexandros Psomas, Athina Terzoglou, Yu Wei, Vassilis Zikas
https://arxiv.org/abs/2506.22089

Pseudo-Equilibria, or: How to Stop Worrying About Crypto and Just Analyze the Game
We consider the problem of a game theorist analyzing a game that uses cryptographic protocols. Ideally, a theorist abstracts protocols as ideal, implementation-independent primitives, letting conclusions in the "ideal world" carry over to the "real world." This is crucial, since the game theorist cannot--and should not be expected to--handle full cryptographic complexity. In today's landscape, the rise of distributed ledgers makes a shared language between cryptography and game theory increasin…