Tootfinder

This https://arxiv.org/abs/2312.16282 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Hidden zeros for particle/string amplitudes and the unity of colored scalars, pions and gluons
Recent years have seen the emergence of a new understanding of scattering amplitudes in the simplest theory of colored scalar particles - the Tr$(ϕ^3)$ theory - based on combinatorial and geometric ideas in the kinematic space of scattering data. In this paper we report a surprise: far from the toy model it appears to be, the ''stringy'' Tr$(ϕ^3)$ amplitudes secretly contain the scattering amplitudes for pions, as well as non-supersymmetric gluons, in any number of dimensions. The amplitudes …

This https://arxiv.org/abs/2312.11428 has been replaced.
link: https://scholar.google.com/scholar?q=a

Random surfaces with large systoles
We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their area. This also allows us to prove a new lower bound on the maximal systole of a closed orientable hyperbolic surface of a given genus.

This https://arxiv.org/abs/2309.15002 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hep…

Scalar field Restricted Boltzmann Machine as an ultraviolet regulator
Restricted Boltzmann Machines (RBMs) are well-known tools used in Machine Learning to learn probability distribution functions from data. We analyse RBMs with scalar fields on the nodes from the perspective of lattice field theory. Starting with the simplest case of Gaussian fields, we show that the RBM acts as an ultraviolet regulator, with the cutoff determined by either the number of hidden nodes or a model mass parameter. We verify these ideas in the scalar field case, where the target dist…

This https://arxiv.org/abs/2012.15778 has been replaced.
link: https://scholar.google.com/scholar?q=a

Metaplectic Iwahori Whittaker functions and supersymmetric lattice models
In this paper we compute new values of Iwahori Whittaker functions on $n$-fold metaplectic covers $\widetilde{G}$ of $\mathbf{G}(F)$ with $\mathbf{G}$ a split reductive group over a non-archimedean local field $F$. For every Iwahori Whittaker function $ϕ$, and for every $g\in\widetilde{G}$, we evaluate $ϕ(g)$ by recurrence relations over the Weyl group using novel "vector Demazure-Whittaker operators." The general formula and strategy of proof are inspired by ideas appearing in the theory of …

Extension of Hayward black hole in $f(R)$ gravity coupled with a scalar field
G. G. L. Nashed
https://arxiv.org/abs/2404.16081 https://

Extension of Hayward black hole in $f(R)$ gravity coupled with a scalar field
This study looks into regular solutions in a theory of gravity called $f(R)$ gravity, which also involves a scalar field. The $f(R)$ theory changes Einstein's ideas by adding a new function related to something called the Ricci scalar. This lets us tweak the equations that describe how gravity works. Adding a scalar field makes the theory more interesting, giving us more ways to investigate and understand it. { The main goal of this research is to create regular black holes using a combination …

This https://arxiv.org/abs/2303.07008 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Status substitution and conspicuous consumption
This paper adapts ideas from social identity theory to set out a new framework for modelling conspicuous consumption. Agents derive status from their own conspicuous consumption and from belonging to an identity group with high conspicuous consumption. Importantly, these two sources of status are substitutes. Agents also feel pressure to conform with their neighbours in a network. This framework can rationalise a set of seemingly conflicting stylised facts about conspicuous consumption that are…

This https://arxiv.org/abs/2402.12638 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Social Mechanics
Social physics is the application of ideas, concepts and tools from physics to study social phenomena. In this article, we present a mechanical theory underlying a mathematical treatment of social physics. We explore the possibility of using fundamental concepts like position, motion, inertia, and interaction, to effectively regard social phenomena analogously to particles interacting with each other in physics. From these concepts, along with heuristics of social change, we investigate the not…

Arrow-Sen theory simplified
Branislav Bori\v{c}i\'c
https://arxiv.org/abs/2404.09018 https://arxiv.org/pdf/2404.09018

Arrow-Sen theory simplified
The traditional Arrow--Sen Social Choice Theory $\bf{TSCT}$ is a mathematical theory built apparently on higher--order formal language. In this paper, we propose a reformulation and reclassification of the $\bf{TSCT}$ axioms in order to obtain a simpler theory based on the first--order language axioms, keeping the spirit of original ideas. This new theory, called Simplified Social Choice Theory, denoted by $\bf{SSCT}$, presents a sub--theory of $\bf{TSCT}$. Roughly speaking, we extract all quat…

Proving the Duffin-Schaeffer conjecture without GCD graphs
Manuel Hauke, Santiago Vazquez Saez, Aled Walker
https://arxiv.org/abs/2404.15123 https://

Proving the Duffin-Schaeffer conjecture without GCD graphs
We present a novel proof of the Duffin-Schaeffer conjecture in metric Diophantine approximation. Our proof is heavily motivated by the ideas of Koukoulopoulos-Maynard's breakthrough first argument, but simplifies and strengthens several technical aspects. In particular, we avoid any direct handling of GCD graphs and their `quality'. We also consider the metric quantitative theory of Diophantine approximations, improving the $(\log Ψ(N))^{-C}$ error-term of Aistleitner-Borda and the first named…

This https://arxiv.org/abs/2401.05526 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Arithmetic, interpolation and factorization of amalgams
Building upon Bennett's and Grosse-Erdmann's ideas falling under the conceptual umbrella of factorization of inequalities, we propose a unified approach towards the structure of certain Banach ideal spaces defined in terms of the least decreasing majorant. The key to our results, and, it seems, the main novelty in general, is the synthesis of discretization process, usually called the blocking technique, along with some tools from the interpolation theory. This blend allows us to obtain an abst…

I'm teaching elementary sampling theory again, using simulations to demonstrate the ideas.
I find I have to revise claims I used to make, e.g.:
"for small samples, the sampling distribution is wider than that implied by the normal distribution & hence we use the t-distribution"
Not true: on 100000 runs the simulated standard deviation of the mean of a uniform 0-1 variable for N=4, is 0.14438 against a theoretical 0.14434.
We use the t-dist because t…

A symbolic information approach applied to human intracranial data to characterize and distinguish different congnitive processes
\'Icaro Rodolfo Soares Coelho Da Paz, Pedro F. A. Silva, Helena Bordini de Lucas, S\'ergio H. A. Lira, Osvaldo A. Rosso, Fernanda Selingardi Matias
https://arxiv.org/abs/2404.17981

A symbolic information approach applied to human intracranial data to characterize and distinguish different congnitive processes
How the human brain processes information during different cognitive tasks is one of the greatest questions in contemporary neuroscience. Understanding the statistical properties of brain signals during specific activities is one promising way to address this question. Here we analyze freely available data from implanted electrocorticography (ECoG) in five human subjects during two different cognitive tasks in the light of information theory quantifiers ideas. We employ a symbolic information a…

Trace formula and Levinson's theorem as an index pairing in the presence of resonances
Angus Alexander
https://arxiv.org/abs/2402.15979 https://…

Trace formula and Levinson's theorem as an index pairing in the presence of resonances
We realise the number of bound states of a Schrödinger operator on $\mathbb{R}^n$ as an index pairing in all dimensions. Expanding on ideas of Guillopé and others, we use high-energy corrections to find representatives of the $K$-theory class of the scattering operator. These representatives allow us to compute the number of bound states using an integral formula involving heat kernel coefficients.

This https://arxiv.org/abs/2312.16915 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Projective Fraïssé limits of trees with confluent epimorphisms
We continue the study of projective Fraïssé limits developed by Irwin-Solecki and Panagiotopoulos-Solecki by investigating families of epimorphisms between finite trees and finite rooted trees. Ideas of monotone, confluent, and light mappings from continuum theory as well as several properties of continua are modified so as to apply them to topological graphs. As the topological realizations of the projective Fraïssé limits we obtain the dendrite $D_3$, the Mohler-Nikiel universal dendroid,…

Review on the probabilistic construction and Conformal bootstrap in Liouville Theory
Colin Guillarmou, Antti Kupiainen, R\'emi Rhodes
https://arxiv.org/abs/2403.12780

Review on the probabilistic construction and Conformal bootstrap in Liouville Theory
In the paper, we review the recent construction of the Liouville conformal field theory (CFT) from probabilistic methods, and the formalization of the conformal bootstrap. This model has offered a fruitful playground to unify the probabilistic construction of the path integral, the geometric axiomatics of CFT by Segal and the representation theoretical content of the conformal bootstrap. We explain and extract the main steps and ideas behind the construction and resolution of this non-compact C…

On the functoriality of refined unramified cohomology
Kees Kok, Lin Zhou
https://arxiv.org/abs/2403.10198 https://arxiv.org/pdf/2403.…

On the functoriality of refined unramified cohomology
In this paper, we generalise the construction of the functorial pullback of refined unramified cohomology between smooth schemes, by following the ideas of Fulton's intersection theory and Rost's cycle modules. We also define standard actions of algebraic cycles on the refined unramified cohomology groups of smooth proper schemes avoiding Chow's moving lemma, which coincide with Schreieder's constructions for smooth projective schemes. As applications, we prove the projective bundle and blow-up…

Towards a representer theorem for identification of passive systems
Brayan M. Shali, Henk J. van Waarde
https://arxiv.org/abs/2404.08297 https://

Towards a representer theorem for identification of passive systems
A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this paper, we present first steps towards tackling this problem for passive systems. In particular, using ideas from the theory of reproducing kernel Hilbert spaces, we solve the problem of identifying a nonnegative input-output operator from data consisting of input-output trajectories of the system. We prove a repr…

This https://arxiv.org/abs/2312.10881 has been replaced.
link: https://scholar.google.com/scholar?q=a

Dirac walks on regular trees
The study of matter fields on an ensemble of random geometries is a difficult problem still in need of new methods and ideas. We will follow a point of view inspired by probability theory techniques that relies on an expansion of the two point function as a sum over random walks. An analogous expansion for Fermions on non-Euclidean geometries is still lacking. Casiday et al. [\textit{Laplace and Dirac operators on graphs}, Linear and Multilinear Algebra (2022) 1] proposed a classical "Dirac wal…

This https://arxiv.org/abs/2312.16915 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Projective Fraïssé limits of trees with confluent epimorphisms
We continue the study of projective Fraïssé limits developed by Irwin-Solecki and Panagiotopoulos-Solecki by investigating families of epimorphisms between finite trees and finite rooted trees. Ideas of monotone, confluent, and light mappings from continuum theory as well as several properties of continua are modified so as to apply them to topological graphs. As the topological realizations of the projective Fraïssé limits we obtain the dendrite $D_3$, the Mohler-Nikiel universal dendroid,…

On the first $\tau$-tilting Hochschild cohomology of an algebra
Claude Cibils, Marcelo Lanzilotta, Eduardo N. Marcos, Andrea Solotar
https://arxiv.org/abs/2404.06916

On the first $τ$-tilting Hochschild cohomology of an algebra
In this paper we introduce, according to one of the main ideas of $τ$-tilting theory, the $τ$-tilting Hochschild cohomology in degree one of a finite dimensional $k$-algebra $\la$, where $k$ is a field. We define the excess of $\la$ as the difference between the dimensions of the $τ$-tilting Hochschild cohomology in degree one and the dimension of the usual Hochschild cohomology in degree one. One of the main results is that for a zero excess bound quiver algebra $\la=kQ/I$, the Hochschild…

This https://arxiv.org/abs/2009.13870 has been replaced.
link: https://scholar.google.com/scholar?q=a

Extending Hrushovski's groupoid-cover correspondence using simplicial groupoids
Hrushovski's suggestion, given in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics , 2012], to capture the structure of the 1-analysable covers of a theory T using simplicial groupoids definable in T is realized here. The ideas of Haykazyan and Moosa, found in ["Functoriality and uniformity in Hrushovski's groupoid-cover correspondence," Annals of Pure and Applied Logic , 2018] are used, and extended, to define an equivalence of categories. Finally, a couple of exam…

This https://arxiv.org/abs/2402.16839 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDL_…

Can Generative AI Generate Breakthrough Ideas?
The surge in generative AI capabilities has affected sectors such as drug discovery and creative text generation, fueling widespread enthusiasm about its potential to revolutionize scientific discovery through efficient exploration of knowledge combinations. But is this belief well-founded? This belief is rooted in the recombinant growth theory, which posits that innovation accelerates when existing ideas are iteratively combined. However, the theory encounters two significant challenges in und…

This https://arxiv.org/abs/2208.01767 has been replaced.
link: https://scholar.google.com/scholar?q=a

Elementary spectral invariants and quantitative closing lemmas for contact three-manifolds
In a previous paper, we defined an "elementary" alternative to the ECH capacities of symplectic four-manifolds, using max-min energy of holomorphic curves subject to point constraints, and avoiding the use of Seiberg-Witten theory. In the present paper we use a variant of this construction to define an alternative to the ECH spectrum of a contact three-manifold. The alternative spectrum has applications to Reeb dynamics in three dimensions. In particular, we adapt ideas from a previous joint pa…

Rough path theory
Ilya Chevyrev
https://arxiv.org/abs/2402.10331 https://arxiv.org/pdf/2402.10331

Rough path theory
The theory of rough paths arose from a desire to establish continuity properties of ordinary differential equations involving terms of low regularity. While essentially an analytic theory, its main motivation and applications are in stochastic analysis, where it has given a new perspective on Itô calculus and a meaning to stochastic differential equations driven by irregular paths outside the setting of semi-martingales. In this survey, we present some of the main ideas that enter rough path t…

Again shamelessly copying from the excellent ideas of @…, I’ve updated my wavefunction collapse code to allow edge-constraints which then let you generate tileable output and then you can make cube nets from them.
In theory you can print, cut, and glue this to get your own CarcoCube™. Probably wants to be cardboard rather than printer pap…

This https://arxiv.org/abs/2312.07909 has been replaced.
initial toot: https://mastoxiv.page/@a…

Ideas of lattice-basis reduction theory for error-stable Bravais lattice determination and ab-initio indexing
In ab-initio indexing, for a given diffraction/scattering pattern, the unit-cell parameters and the Miller indices assigned to reflections in the pattern are determined simultaneously. "Ab-initio" means a process performed without any good prior information on the crystal lattice. Newly developed ab-initio indexing software is frequently reported in crystallography. However, it is not widely recognized that use of a Bravais lattice determination method, which is tolerant to experimental errors,…

Towards a representer theorem for identification of passive systems
Brayan M. Shali, Henk J. van Waarde
https://arxiv.org/abs/2404.08297 https://

Towards a representer theorem for identification of passive systems
A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this paper, we present first steps towards tackling this problem for passive systems. In particular, using ideas from the theory of reproducing kernel Hilbert spaces, we solve the problem of identifying a nonnegative input-output operator from data consisting of input-output trajectories of the system. We prove a repr…

Global controllability to harmonic maps of the heat flow from a circle to a sphere
Jean-Michel Coron, Shengquan Xiang
https://arxiv.org/abs/2402.08990 http…

Global controllability to harmonic maps of the heat flow from a circle to a sphere
In this paper, we study the global controllability and stabilization problems of the harmonic map heat flow from a circle to a sphere. Combining ideas from control theory, heat flow, differential geometry, and asymptotic analysis, we obtain several important properties, such as small-time local controllability, local quantitative rapid stabilization, obstruction to semi-global asymptotic stabilization, and global controllability to geodesics. Surprisingly, due to the geometric feature of the eq…

This https://arxiv.org/abs/2205.00879 has been replaced.
link: https://scholar.google.com/scholar?q=a

An invitation to formal power series
This is a lecture on the theory of formal power series developed entirely without any analytic machinery. Combining ideas from various authors we are able to prove Newton's binomial theorem, Jacobi's triple product, the Rogers--Ramanujan identities and many other prominent results. We apply these methods to derive several combinatorial theorems including Ramanujan's partition congruences, generating functions of Stirling numbers and Jacobi's four-square theorem. We further discuss formal Lauren…

Social Mechanics
VS Morales-Salgado
https://arxiv.org/abs/2402.12638 https://arxiv.org/pdf/2402.12638<…

Social Mechanics
Social physics is the application of ideas, concepts and tools from physics to study social phenomena. In this article, we present a mechanical theory underlying a mathematical treatment of social physics. We explore the possibility of using fundamental concepts like position, motion, inertia, and interaction, to effectively regard social phenomena analogously to particles interacting with each other in physics. From these concepts, along with heuristics of social change, we investigate the not…

This https://arxiv.org/abs/2306.06054 has been replaced.
initial toot: https://mastoxiv.page/@…

Exact partition function of the Potts model on the Sierpinski gasket and the Hanoi lattice
We present an analytic study of the Potts model partition function on the Sierpinski and Hanoi lattices, which are self-similar lattices of triangular shape with non integer Hausdorff dimension. Both lattices are examples of non-trivial thermodynamics in less than two dimensions, where mean field theory does not apply. We used and explain a method based on ideas of graph theory and renormalization group theory to derive exact equations for appropriate variables that are similar to the restricte…

This https://arxiv.org/abs/2404.10196 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Yang-Mills-Higgs Equations on Spherical Orbifolds
In this paper we study (static) solutions of the rank 2 Yang-Mills-Higgs equations on the Riemann sphere, with concical singularities, that bifurcate from constant curvature connections. We focus attention on the case where there are exactly four such singularities. This study brings together ideas from the gauge theory of constant curvature connections on vector bundles over singular Riemann surfaces with the Riemann-Hilbert analysis of classical Fuchsian ODEs.

Tropical Amplitudes For Colored Lagrangians
Nima Arkani-Hamed, Carolina Figueiredo, Hadleigh Frost, Giulio Salvatori
https://arxiv.org/abs/2402.06719 https…

Tropical Amplitudes For Colored Lagrangians
Recently a new formulation for scattering amplitudes in Tr($Φ^3$) theory has been given based on simple combinatorial ideas in the space of kinematic data. This allows all-loop integrated amplitudes to be expressed as ''curve integrals'' defined using tropical building blocks - the ''headlight functions''. This paper shows how the formulation extends to the amplitudes of more general Lagrangians. We will present a number of different ways of introducing tropical ''numerator functions'' that al…

This https://arxiv.org/abs/2306.06054 has been replaced.
initial toot: https://mastoxiv.page/@…

Exact partition function of the Potts model on the Sierpinski gasket and the Hanoi lattice
We present an analytic study of the Potts model partition function on the Sierpinski and Hanoi lattices, which are self-similar lattices of triangular shape with non integer Hausdorff dimension. Both lattices are examples of non-trivial thermodynamics in less than two dimensions, where mean field theory does not apply. We used and explain a method based on ideas of graph theory and renormalization group theory to derive exact equations for appropriate variables that are similar to the restricte…

Hunter's positivity theorem and random vector norms
Ludovick Bouthat, \'Angel Ch\'avez, Stephan Ramon Garcia
https://arxiv.org/abs/2403.10314 h…

Hunter's positivity theorem and random vector norms
A theorem of Hunter ensures that the complete homogeneous symmetric polynomials of even degree are positive definite functions. A probabilistic interpretation of Hunter's theorem suggests a broad generalization: the construction of so-called random vector norms on square complex matrices. This paper surveys these ideas, starting from the fundamental notions and developing the theory to its present state. We study numerous examples and present a host of open problems.

Yang-Mills-Higgs Equations on Spherical Orbifolds
Nicholas M. Ercolani
https://arxiv.org/abs/2404.10196 https://arxiv.org/pdf/2404.10…

Yang-Mills-Higgs Equations on Spherical Orbifolds
In this paper we study (static) solutions of the rank 2 Yang-Mills-Higgs equations on the Riemann sphere, with concical singularities, that bifurcate from constant curvature connections. We focus attention on the case where there are exactly four such singularities. This study brings together ideas from the gauge theory of constant curvature connections on vector bundles over singular Riemann surfaces with the Riemann-Hilbert analysis of classical Fuchsian ODEs.

This https://arxiv.org/abs/2312.07909 has been replaced.
initial toot: https://mastoxiv.page/@a…

Ideas of lattice-basis reduction theory for error-stable Bravais lattice determination and ab-initio indexing
Although newly developed indexing software is frequently reported in crystallography, it is not widely recognized that the use of error-stable Bravais lattice determinations can simplify indexing algorithms and increase their success rates. In indexing, a code for error-stable unit-cell identification is also required to exclude duplicate solutions. One of our goals is to collect information on the lattice-basis reduction theory and its application to these analyses. The main result is an err…

This https://arxiv.org/abs/2311.12103 has been replaced.
initial toot: https://mastoxiv.page/@ar…

A tensor network view of multilayer multiconfiguration time-dependent Hartree methods
The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method and the density matrix renormalization group (DMRG) are powerful workhorses applied mostly in different scientific fields. Although both methods are based on tensor network states, very different mathematical languages are used for describing them. This severely limits knowledge transfer and sometimes leads to re-inventions of ideas well known in the other field. Here, we review ML-MCTDH and DMRG theory using both MCTDH …

This https://arxiv.org/abs/2312.07909 has been replaced.
initial toot: https://mastoxiv.page/@a…

Ideas of lattice-basis reduction theory for error-stable Bravais lattice determination and ab-initio indexing
Although newly developed indexing software is frequently reported in crystallography, it is not widely recognized that the use of error-stable Bravais lattice determinations can simplify indexing algorithms and increase their success rates. In indexing, a code for error-stable unit-cell identification is also required to exclude duplicate solutions. One of our goals is to collect information on the lattice-basis reduction theory and its application to these analyses. The main result is an err…

This https://arxiv.org/abs/2403.06652 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Symmetry Resolved Measures in Quantum Field Theory: a Short Review
In this short review we present the key definitions, ideas and techniques involved in the study of symmetry resolved entanglement measures, with a focus on the symmetry resolved entanglement entropy. In order to be able to define such entanglement measures, it is essential that the theory under study possess an internal symmetry. Then, symmetry resolved entanglement measures quantify the contribution to a particular entanglement measure that can be associated to a chosen symmetry sector. Our re…

This https://arxiv.org/abs/2403.06652 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Symmetry Resolved Measures in Quantum Field Theory: a Short Review
In this short review we present the key definitions, ideas and techniques involved in the study of symmetry resolved entanglement measures, with a focus on the symmetry resolved entanglement entropy. In order to be able to define such entanglement measures, it is essential that the theory under study possess an internal symmetry. Then, symmetry resolved entanglement measures quantify the contribution to a particular entanglement measure that can be associated to a chosen symmetry sector. Our re…