Tootfinder

This https://arxiv.org/abs/0811.2774 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

A minimalist two-level foundation for constructive mathematics
We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin. One level is given by an intensional type theory, called Minimal type theory. This theory extends the set-theoretic version introduced in the mentioned paper with collections. The other level is given by an extensional set theory which is interpreted in the first one by means of a quotient model. This two-level theory has two main features: it is minimal among the most relevant f…

The dual role of constructive agents in public goods games: limited alone, amplifying cooperation with destructive agents
Yuting Dong, Zhixue He, Chen Shen, Lei Shi, Jun Tanimoto
https://arxiv.org/abs/2404.01637

The dual role of constructive agents in public goods games: limited alone, amplifying cooperation with destructive agents
Recent studies have revealed a paradoxical phenomenon in public goods games, wherein destructive agents, harming both cooperators and defectors, can unexpectedly bolster cooperation. Building upon this intriguing premise, our paper introduces a novel concept: constructive agents, which confer additional benefits to both cooperators and defectors. We investigate the impact of these agents on cooperation dynamics within the framework of public goods games. Employing replicator dynamics, we find t…

C Concepts. Good in concept.
OK, OK. It's a good start. Late start, but a good start.
#cpp #cPlusPlus #programming

This https://arxiv.org/abs/2403.04618 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csPL_…

Strong Priority and Determinacy in Timed CCS
Building on the standard theory of process algebra with priorities, we identify a new scheduling mechanism, called "constructive reduction" which is designed to capture the essence of synchronous programming. The distinctive property of this evaluation strategy is to achieve determinacy-by-construction for multi-cast concurrent communication with shared memory. In the technical setting of CCS extended by clocks and priorities, we prove for a large class of "coherent" processes a confluence prop…

This https://arxiv.org/abs/0811.2774 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

A minimalist two-level foundation for constructive mathematics
We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin. One level is given by an intensional type theory, called Minimal type theory. This theory extends the set-theoretic version introduced in the mentioned paper with collections. The other level is given by an extensional set theory which is interpreted in the first one by means of a quotient model. This two-level theory has two main features: it is minimal among the most relevant f…

Constructive vs Predicative data: #Programmers, but especially my

This https://arxiv.org/abs/2208.04984 has been replaced.
link: https://scholar.google.com/scholar?q=a

Constructive exceptional bundles on $\mathbb{P}^3$
We give a complete classification of the Chern characters of constructive exceptional vector bundles on $\mathbb{P}^3$ analogous to the work of Drézet and Le Potier on $\mathbb{P}^2$, and using this classification prove that a constructive exceptional bundle $E$ on $\mathbb{P}^3$ with $μ(E) \geq 0$ is globally generated.

This https://arxiv.org/abs/2403.12804 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Bayes Principle and Segal Axioms for $P(ϕ)_2$, with application to Periodic Covers
The goal of the present paper is to reconcile the so-called $P(ϕ)_2$ model from classical constructive quantum field theory (CQFT) with (metric version of) geometric and categorical axioms proposed by G. Segal (see refs in Kontsevich and Segal arXiv:2105.10161) in the 90's, in showing that the $P(ϕ)_2$ model satisfies these axioms, appropriately adjusted. The approach is based on previous works of Dimock arXiv:math-ph/0305017 and Pickrell arXiv:math-ph/0702077, while we give a new proof to a …

This https://arxiv.org/abs/2402.06153 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Complex saddles of the Veneziano amplitude
Saddle point approximation is a useful method to explore high energy asymptotic behaviors of string scattering amplitudes. We show that, even at tree-level, there are infinitely many complex saddles contributing to string scattering amplitudes, and that the complex saddles reproduce their appropriate poles and zeros. Each complex saddle is interpreted as a semi-classical path of a string in Lorentzian signature. The poles and zeros of the Veneziano amplitude are understood as constructive or de…

Smoothly slice links in $S^2 \times S^2$ or $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$
Marco Marengon, Clayton McDonald
https://arxiv.org/abs/2403.00057 h…

Smoothly slice links in $S^2 \times S^2$ or $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$
For $X = S^2 \times S^2$ and $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$, we show that there exists a link with 2 components which is not smoothly slice in $X$. By contrast, it is well-known that every knot (i.e., link with 1 component) is smoothly slice in both $S^2 \times S^2$ and $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$. Our proof uses classical topological and smooth obstructions, as well as constructive arguments to exploit the symmetries of the problem. As a side note, we also show tha…

This https://arxiv.org/abs/2311.15495 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Constructive Proof of the Spherical Parisi Formula
The Parisi formula for the free energy is among the crown jewels in the theory of spin glasses. We present a simpler proof of the lower bound in the case of the spherical mean-field model. Our method follows the TAP approach developed recently in e.g. (Subag, 2018): we obtain an ultrametric tree of pure states, each with approximately the same free energy as the entire model, which are hierarchically arranged in accordance with the Parisi ansatz. We construct this tree ``layer by layer'' given …

Characterization of Matrices Satisfying the Reverse Order Law for the Moore-Penrose Pseudoinverse
Oskar K\k{e}dzierski
https://arxiv.org/abs/2404.02843 htt…

Characterization of Matrices Satisfying the Reverse Order Law for the Moore-Penrose Pseudoinverse
We give a constructive characterization of matrices satisfying the reverse-order law for the Moore--Penrose pseudoinverse. In particular, for a given matrix $A$ we construct another matrix $B$, of arbitrary compatible size and chosen rank, in terms of the right singular vectors of $A$, such that the reverse order law for $AB$ is satisfied. Moreover, we show that any matrix satisfying this law comes from a similar construction. As a consequence, several equivalent conditions to $B^+ A^+$ being a…

This https://arxiv.org/abs/2303.08633 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Expected Utility from a Constructive Viewpoint
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs is intuitionistic. In a second sense of the word, ``constructive'' is taken to mean ``built up from smaller components.'' Lotteries as well as preferences vary continuously over some topological space. The topology encodes observability or verifiability restr…

This https://arxiv.org/abs/2312.17023 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tensorial structure of the lifting doctrine in constructive domain theory
We present a survey of the two-dimensional and tensorial structure of the lifting doctrine in constructive domain theory, i.e. in the theory of directed-complete partial orders (dcpos) over an arbitrary elementary topos. We establish the universal property of lifting of dcpos as the Sierpiński cone, from which we deduce (1) that lifting forms a Kock-Zöberlein doctrine, (2) that lifting algebras, pointed dcpos, and inductive partial orders form canonically equivalent locally posetal 2-categori…

I have given evidence to Oireachtas Committees quite a few times over the years. They have run the gamut from professional, inquiring and constructive to, um, not that.
The format relies entirely on the legislators attending wanting to make it work and respecting their witnesses (even if not agreeing with them).
Having voluntary witnesses refuse to attend for fear of being mistreated undermines the opportunities for those constructive inquiries.
https://www.irishtimes.com/opinion/2024/02/24/youd-be-out-of-your-mind-to-go-there-how-public-servants-really-feel-about-oireachtas-committees/

{constructive} prints code that can be used to recreate R objects. Like dput, but better... #rstats

A Constructive Real Projective Plane
Mark Mandelkern
https://arxiv.org/abs/2404.16979 https://arxiv.org/pdf/2404.16979

A Constructive Real Projective Plane
The classical theory of plane projective geometry is examined constructively, using both synthetic and analytic methods. The topics include Desargues's Theorem, harmonic conjugates, projectivities, involutions, conics, Pascal's Theorem, poles and polars. The axioms used for the synthetic treatment are constructive versions of the traditional axioms. The analytic construction is used to verify the consistency of the axioms; it is based on the usual model in three-dimensional Euclidean space, usi…

Interpretation of Inaccessible Sets in Martin-L\"{o}f Type Theory with One Mahlo Universe
Yuta Takahashi
https://arxiv.org/abs/2402.15074 https://

Interpretation of Inaccessible Sets in Martin-Löf Type Theory with One Mahlo Universe
Martin-Löf type theory $\mathbf{MLTT}$ was extended by Setzer with the so-called Mahlo universe types. This extension is called $\mathbf{MLM}$ and was introduced to develop a variant of $\mathbf{MLTT}$ equipped with an analogue of a large cardinal. Another instance of constructive systems extended with an analogue of a large set was formulated in the context of Aczel's constructive set theory: $\mathbf{CZF}$. Rathjen, Griffor and Palmgren extended $\mathbf{CZF}$ with inaccessible sets of all t…

/A Non-Constructive Topological Proof that 2^(2^2) 1 is Prime/
#OddDissertationTopics #HashtagGames

This https://arxiv.org/abs/2311.06687 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Conditions when the problems of linear programming are algorithmically unsolvable
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number components. We show that it is impossible to have an algorithm that solves an arbitrary constructive real programming problem.

Congratulations to Dr. Keri Day '04 M.A.R., recently inaugurated by Princeton Theology Seminary as Professor of Constructive Theology and African American Religion — the first Black woman in the seminary's history to be promoted to full professor!
https://buff.ly/44hcNns

You have no idea how much I love and appreciate _concrete_ helpful & constructive feedback like "put import statements in code snippets" compared to handwavy & obtuse comments like "the docs are pretty bad..." or "examples are all for wild or out there things but what I need are tutorials on the basics". None of the hundreds of example projects & snippets cover those, are you sure?!
Concrete feedback (like the former) actually helps kickstartin…

thi-ng umbrella · Discussions
Explore the GitHub Discussions forum for thi-ng umbrella. Discuss code, ask questions & collaborate with the developer community.

This https://arxiv.org/abs/2306.02149 has been replaced.
link: https://scholar.google.com/scholar?q=a

A General Framework for Interpretable Neural Learning based on Local Information-Theoretic Goal Functions
Despite the impressive performance of biological and artificial networks, an intuitive understanding of how their local learning dynamics contribute to network-level task solutions remains a challenge to this date. Efforts to bring learning to a more local scale indeed lead to valuable insights, however, a general constructive approach to describe local learning goals that is both interpretable and adaptable across diverse tasks is still missing. We have previously formulated a local informatio…

This https://arxiv.org/abs/2302.00151 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Formalising and Computing the Fourth Homotopy Group of the $3$-Sphere in Cubical Agda
Brunerie's 2016 PhD thesis contains the first synthetic proof in Homotopy Type Theory (HoTT) of the classical result that the fourth homotopy group of the 3-sphere is $\mathbb{Z}/2\mathbb{Z}$. The proof is one of the most impressive pieces of synthetic homotopy theory to date and uses a lot of advanced classical algebraic topology rephrased synthetically. Furthermore, the proof is fully constructive and the main result can be reduced to the question of whether a particular "Brunerie number" $β…

I have given evidence to Oireachtas Committees quite a few times over the years. They have run the gamut from professional, inquiring and constructive to, um, not that.
The format relies entirely on the legislators attending wanting to make it work and respecting their witnesses (even if not agreeing with them).
Having voluntary witnesses refuse to attend for fear of being mistreated undermines the opportunities for those constructive inquiries.
https://www.irishtimes.com/opinion/2024/02/24/youd-be-out-of-your-mind-to-go-there-how-public-servants-really-feel-about-oireachtas-committees/

It's important to be able to tell constructive criticism from fascism.
Constructive criticism is backed by valid arguments. It permits counterarguments, as well as straight rejection if the rights of others aren't affected ("you are probably right that Y would be better, but X works for me").
Fascism is based upon "because I do it like this", and "I think it should be like this".
This toot is sponsored by the criticism in the question of "why are you cutting that tomato into such thick slices [for your own bread]?"

Contactifications: a Lagrangian description of compact Hamiltonian systems
Katarzyna Grabowska, Janusz Grabowski, Marek Ku\'s, Giuseppe Marmo
https://arxiv.org/abs/2404.19560 https://arxiv.org/pdf/2404.19560
arXiv:2404.19560v1 Announce Type: new
Abstract: If $\eta$ is a contact form on a manifold $M$ such that the orbits of the Reeb vector field form a simple foliation $\mathcal{F}$ on $M$, then the presymplectic 2-form $d\eta$ on $M$ induces a symplectic structure $\omega$ on the quotient manifold $N=M/\mathcal{F}$. We call $(M,\eta)$ a $\textit contactification$ of the symplectic manifold $(N,\omega)$. First, we present an explicit geometric construction of contactifications of some coadjoint orbits of connected Lie groups. Our construction is a far going generalization of the well-known contactification of the complex projective space $\mathbb{C}P^{n-1}$, being the unit sphere $S^{2n-1}$ in $\mathbb{C}^{n}$, and equipped with the restriction of the Liouville 1-form on $\mathbb{C}^n$. Second, we describe a constructive procedure for obtaining contactification in the process of the Marsden-Weinstein-Meyer symplectic reduction and indicate geometric obstructions for the existence of compact contactifications. Third, we show that contactifications provide a nice geometrical tool for a Lagrangian description of Hamiltonian systems on compact symplectic manifolds $(N,\omega)$, on which symplectic forms never admit a `vector potential'.

Decoding Radiologists' Intentions: A Novel System for Accurate Region Identification in Chest X-ray Image Analysis
Akash Awasthi, Safwan Ahmad, Bryant Le, Hien Van Nguyen
https://arxiv.org/abs/2404.18981 https://arxiv.org/pdf/2404.18981
arXiv:2404.18981v1 Announce Type: new
Abstract: In the realm of chest X-ray (CXR) image analysis, radiologists meticulously examine various regions, documenting their observations in reports. The prevalence of errors in CXR diagnoses, particularly among inexperienced radiologists and hospital residents, underscores the importance of understanding radiologists' intentions and the corresponding regions of interest. This understanding is crucial for correcting mistakes by guiding radiologists to the accurate regions of interest, especially in the diagnosis of chest radiograph abnormalities. In response to this imperative, we propose a novel system designed to identify the primary intentions articulated by radiologists in their reports and the corresponding regions of interest in CXR images. This system seeks to elucidate the visual context underlying radiologists' textual findings, with the potential to rectify errors made by less experienced practitioners and direct them to precise regions of interest. Importantly, the proposed system can be instrumental in providing constructive feedback to inexperienced radiologists or junior residents in the hospital, bridging the gap in face-to-face communication. The system represents a valuable tool for enhancing diagnostic accuracy and fostering continuous learning within the medical community.

Hello, Happy! @…
I see you. I hear you! Thank you for piping up! Keep making noise! (GAWD, I need you.) https://happyfedi.better-than.tv/@happ…

Post by Happy, @happy@happyfedi.better-than.tv
🌞 "Hello Fediverse! Just landed here to spread some sunshine. With a strong following elsewhere, I'm here to infuse your timelines with positivity and joy! Amidst all the gloom in the news, let’s create a space filled with constructive vibes and smiles. Let's bring some light into the wo...

Constructive proofs of existence and stability of solitary waves in the capillary-gravity Whitham equation
Matthieu Cadiot
https://arxiv.org/abs/2403.18718

Constructive proofs of existence and stability of solitary waves in the capillary-gravity Whitham equation
In this manuscript, we present a method to prove constructively the existence and spectral stability of solitary waves (solitons) in the capillary-gravity Whitham equation. By employing Fourier series analysis and computer-aided techniques, we successfully approximate the Fourier multiplier operator in this equation, allowing the construction of an approximate inverse for the linearization around an approximate solution $u_0$. Then, using a Newton-Kantorovich approach, we provide a sufficient c…

Online session (free): "Care in Feedback with Writing Diversely" with Renee Harleston
"Learn about sensitivity reading and why this specific type of feedback is important, get tips on how to give respectful and constructive feedback, and consider ways to be a gracious recipient so you can make the most of feedback on your writing."

[[constructive interference]], digital on analog, #2024

This https://arxiv.org/abs/2203.14379 has been replaced.
link: https://scholar.google.com/scholar?q=a

Constructive Separations and Their Consequences
For a complexity class $C$ and language $L$, a constructive separation of $L \notin C$ gives an efficient algorithm (also called a refuter) to find counterexamples (bad inputs) for every $C$-algorithm attempting to decide $L$. We study the questions: Which lower bounds can be made constructive? What are the consequences of constructive separations? We build a case that "constructiveness" serves as a dividing line between many weak lower bounds we know how to prove, and strong lower bounds again…

Constructive Mathematics
Mark Mandelkern
https://arxiv.org/abs/2404.05743 https://arxiv.org/pdf/2404.05743

Constructive Mathematics
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This nontechnical article discusses the motivating ideas behind the constructive approach to mathematics and the implications of constructive mathematics for the history of mathematics.

This https://arxiv.org/abs/2403.04618 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csPL_…

Strong Priority and Determinacy in Timed CCS
Building on the standard theory of process algebra with priorities, we identify a new scheduling mechanism, called "constructive reduction" which is designed to capture the essence of synchronous programming. The distinctive property of this evaluation strategy is to achieve determinacy-by-construction for multi-cast concurrent communication with shared memory. In the technical setting of CCS extended by clocks and priorities, we prove for a large class of "coherent" processes a confluence prop…

This https://arxiv.org/abs/2304.08946 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Uniquely hamiltonian graphs for many sets of degrees
We give constructive proofs for the existence of uniquely hamiltonian graphs for various sets of degrees. We give constructions for all sets with minimum 2 (a trivial case added for completeness), all sets with minimum 3 that contain an even number (for sets without an even number it is known that no uniquely hamiltonian graphs exist), and all sets with minimum 4 and at least two elements, where all degrees different from 4 are at least 10. For minimum degree 3 and 4, the constructions also giv…

You have no idea how much I love and appreciate _concrete_ helpful & constructive feedback like "put import statements in code snippets" compared to handwavy & obtuse comments like "the docs are pretty bad..." or "examples are all for wild or out there things but what I need are tutorials on the basics". None of the hundreds of example projects & snippets cover those, are you sure?!
Concrete feedback (like the former) actually helps kickstartin…

thi-ng umbrella · Discussions
Explore the GitHub Discussions forum for thi-ng umbrella. Discuss code, ask questions & collaborate with the developer community.

This https://arxiv.org/abs/2302.00151 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Formalising and Computing the Fourth Homotopy Group of the $3$-Sphere in Cubical Agda
Brunerie's 2016 PhD thesis contains the first synthetic proof in Homotopy Type Theory (HoTT) of the classical result that the fourth homotopy group of the 3-sphere is $\mathbb{Z}/2\mathbb{Z}$. The proof is one of the most impressive pieces of synthetic homotopy theory to date and uses a lot of advanced classical algebraic topology rephrased synthetically. Furthermore, the proof is fully constructive and the main result can be reduced to the question of whether a particular "Brunerie number" $β…

Imagining a Future of Designing with AI: Dynamic Grounding, Constructive Negotiation, and Sustainable Motivation
Priyan Vaithilingam, Ian Arawjo, Elena L. Glassman
https://arxiv.org/abs/2402.07342

Imagining a Future of Designing with AI: Dynamic Grounding, Constructive Negotiation, and Sustainable Motivation
We ideate a future design workflow that involves AI technology. Drawing from activity and communication theory, we attempt to isolate the new value large AI models can provide design compared to past technologies. We arrive at three affordances -- dynamic grounding, constructive negotiation, and sustainable motivation -- that summarize latent qualities of natural language-enabled foundation models that, if explicitly designed for, can support the process of design. Through design fiction, we th…

I want to promote my ko-fi stuff a bit more, but I'm reluctant to use mainstrram platforms like Inst*gram and Thr*ads because I don't believe in their values or trust them.
As I don’t really do video, I feel that I would be a bit out of place on TikTok and Twitch...
Bluesky is another option, which I am using sometimes... I do need to setup up crossposting somehow... maybe.
Am I missing something?
I am open to constructive suggestions.

Via Vincent Proce on Twitter on AI:
“This is making the rounds!” (On #AIArt)

L\'evy noise-induced coherence resonance in the FitzHugh-Nagumo oscillator: numerical study versus experiment
Ivan Korneev, Anna Zakharova, Vladimir V. Semenov
https://arxiv.org/abs/2402.19426

Lévy noise-induced coherence resonance in the FitzHugh-Nagumo oscillator: numerical study versus experiment
Using a model of the FitzHugh-Nagumo oscillator in the excitable regime, we investigate the influence of the Lévy noise's properties on the effect of coherence resonance. In particular, we demonstrate that the Lévy noise can be a constructive or destructive factor providing for enhancement or suppression of noise-induced coherence. We show that the positive or negative role of the Lévy noise impact is dictated by the noise's stability index and skewness parameter. The correlation time and th…

I have been to contentious Oireachtas Committees and constructive ones. This one was definitely a Constructive meeting.
Both Gov and non-Gov representatives quizzed the panel of speakers, including the Garda commissioner, on both the practicalities of facial recognition technology and the Legals.

Save the whale, just not the planet it lives on…
Am I the only one perturbed by this level of cognitive dissonance?
https://thehill.com/policy/energy-environment/4539845-biden-administration-sued-over-v…

Biden administration sued over Virginia offshore wind farm approval
A conservative think tank on Monday sued the Biden administration in an effort to reverse approval of what would be the largest offshore wind farm of its kind.  The Heartland Institute filed the suit with the Committee for a Constructive Tomorrow, a nonprofit that advocates for an economically libertarian approach to environmental action and has denied…

Online session (free): "Care in Feedback with Writing Diversely" with Renee Harleston
"Learn about sensitivity reading and why this specific type of feedback is important, get tips on how to give respectful and constructive feedback, and consider ways to be a gracious recipient so you can make the most of feedback on your writing."

This https://arxiv.org/abs/2204.10354 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Constructive Proof that Many Groups with Non-Torsion 2-Cohomology are Not Matricially Stable
A discrete group is matricially stable if every function from the group to a complex unitary group that is "almost multiplicative" in the point-operator norm topology is "close" to a genuine unitary representation. It follows from a recent result due to Dadarlat that all amenable, groups with non-torsion integral 2-cohomology are not matricially stable, but the proof does not lead to explicit examples of asymptotic representations that are not perturbable to genuine representations. The purpose…

This https://arxiv.org/abs/2312.17023 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tensorial structure of the lifting doctrine in constructive domain theory
We present a survey of the two-dimensional and tensorial structure of the lifting doctrine in constructive domain theory, i.e. in the theory of directed-complete partial orders (dcpos) over an arbitrary elementary topos. We establish the universal property of lifting of dcpos as the Sierpiński cone, from which we deduce (1) that lifting forms a Kock-Zöberlein doctrine, (2) that lifting algebras, pointed dcpos, and inductive partial orders form canonically equivalent locally posetal 2-categori…

Stability of pairwise social dilemma games: destructive agents, constructive agents, and their joint effects
Khadija Khatun, Chen Shen, Lei Shi, Jun Tanimoto
https://arxiv.org/abs/2402.12809

Stability of pairwise social dilemma games: destructive agents, constructive agents, and their joint effects
Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains inadequately understood, particularly in the context of pairwise social dilemma games and in comparison to their counterparts, constructive agents, who opt out of the game but indiscriminately benefit others. Furthermore, little is known about the combined effects of bo…

This https://arxiv.org/abs/2311.08313 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Fast Track to Full Gold Open Access
The world of scientific publishing is changing; the days of an old type of subscription-based earnings for publishers seem over, and we are entering a new era. It seems as if an ever-increasing number of journals from disparate publishers are going Gold, Open Access that is, yet have we rigorously ascertained the issue in its entirety, or are we touting the strengths and forgetting about constructive criticism and careful weighing of evidence? We will therefore present the current state of the …

Recommendations for accelerating open #preprint #PeerReview to improve the culture of #science: https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.3002502 - "Preprints are enabling new forms of peer review that have the potential to be more thorough, inclusive, and collegial than traditional journal peer review, and to thus fundamentally shift the culture of peer review toward constructive collaboration."

I have been to contentious Oireachtas Committees and constructive ones. This one was definitely a Constructive meeting.
Both Gov and non-Gov representatives quizzed the panel of speakers, including the Garda commissioner, on both the practicalities of facial recognition technology and the Legals.

*Current job satisfaction status*:
Stalking the hallways at work with literal fire pouring out of my orifices like the fucking #Balrog just waiting... *itching* for a senior VP or better the CEO to say anything, *anything* less than brilliantly constructive or helpful like "so when is project x do-" and I get 2 snap and go `ITLL BE DONE WHEN ITS DONE, FUCK OFF TILL THEN!. YOU'VE FUCKIN…

Tangent space generators of matrix product states and exact Floquet quantum scars
Marko Ljubotina, Elena Petrova, Norbert Schuch, Maksym Serbyn
https://arxiv.org/abs/2403.12325

Tangent space generators of matrix product states and exact Floquet quantum scars
The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with time-dependent couplings is a challenging task and very little is known about the existence of solutions and their properties. In this work we develop a constructive approach for preparing matrix product states (MPS) via continuous unitary evolution. We provide …

This https://arxiv.org/abs/2402.03877 has been replaced.
link: https://scholar.google.com/scholar?q=a

Beyond Lines and Circles: Unveiling the Geometric Reasoning Gap in Large Language Models
Large Language Models (LLMs) demonstrate ever-increasing abilities in mathematical and algorithmic tasks, yet their geometric reasoning skills are underexplored. We investigate LLMs' abilities in constructive geometric problem-solving one of the most fundamental steps in the development of human mathematical reasoning. Our work reveals notable challenges that the state-of-the-art LLMs face in this domain despite many successes in similar areas. LLMs exhibit biases in target variable selection a…

This https://arxiv.org/abs/2301.06546 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multivariate Hensel Lemma for ultrametric fields
The Multivariate Hensel Lemma for local rings is usually proved as a consequence of the Grothendieck version of Zariski's Main Theorem. This version deals with a more general situation that is a priori much more difficult. In this paper, we give a direct proof of the Multivariate Hensel Lemma for ultrametric fields, in the framework of constructive mathematics and without using~ZMT. In the framework of classical mathematics, our result entails the Lemma for rank-one valued fields.

This https://arxiv.org/abs/2302.14699 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Analysis of Tennenbaum's Theorem in Constructive Type Theory
Tennenbaum's theorem states that the only countable model of Peano arithmetic (PA) with computable arithmetical operations is the standard model of natural numbers. In this paper, we use constructive type theory as a framework to revisit, analyze and generalize this result. The chosen framework allows for a synthetic approach to computability theory, exploiting that, externally, all functions definable in constructive type theory can be shown computable. We then build on this viewpoint, and fur…

Dynamic fluctuation-dissipation theory for Generalized Langevin Equations: constructive constraints, stability and realizability
Massimiliano Giona, Giuseppe Procopio, Chiara Pezzotti
https://arxiv.org/abs/2403.05431

Dynamic fluctuation-dissipation theory for Generalized Langevin Equations: constructive constraints, stability and realizability
Using the initial-value formulation, a dynamic theory for systems evolving according to a Generalized Langevin Equation is developed, providing more restrictive conditions on the existence of equilibrium behavior and its fluctuation-dissipation implications. For systems fulfilling the property of local realizability, that for all the practical purposes corresponds to the postulate of the existence of a Markovian embedding, physical constraints, expressed in the form of dissipative stability a…

Constructive Coordinatization of Desarguesian Planes
Mark Mandelkern
https://arxiv.org/abs/2402.07382 https://arxiv.org/pdf/2402.0738…

Constructive Coordinatization of Desarguesian Planes
A classical theory of Desarguesian geometry, originating with D. Hilbert in his 1899 treatise, Grundlagen der Geometrie, leads from axioms to the construction of a division ring from which coordinates may be assigned to points, and equations to lines; this theory is highly nonconstructive. The present paper develops this coordinatization theory constructively, in accordance with the principles introduced by Errett Bishop in his 1967 book, Foundations of Constructive Analysis. The traditional ge…

Stationary non-radial localized patterns in the planar Swift-Hohenberg PDE: constructive proofs of existence
Matthieu Cadiot, Jean-Philippe Lessard, Jean-Christophe Nave
https://arxiv.org/abs/2403.10450

Stationary non-radial localized patterns in the planar Swift-Hohenberg PDE: constructive proofs of existence
In this paper, we present a methodology for establishing constructive proofs of existence of smooth, stationary, non-radial localized patterns in the planar Swift-Hohenberg equation. Specifically, given an approximate solution $u_0$, we construct an approximate inverse for the linearization around $u_0$, enabling the development of a Newton-Kantorovich approach. Consequently, we derive a sufficient condition for the existence of a unique localized pattern in the vicinity of $u_0$. The verificat…

This https://arxiv.org/abs/2403.00201 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Constructive S4 modal logics with the finite birelational frame property
The logics $\mathsf{CS4}$ and $\mathsf{IS4}$ are the two leading intuitionistic variants of the modal logic $\mathsf{S4}$. Whether the finite model property holds for each of these logics have been long-standing open problems. It was recently shown that $\mathsf{IS4}$ has the finite frame property and thus the finite model property. In this paper, we prove that $\mathsf{CS4}$ also enjoys the finite frame property. Additionally, we investigate the following three logics closely related to $\ma…

Pairing enhancement through the photography of the intermediate nucleus spectrum in a two-nucleon transfer process
G. Singh
https://arxiv.org/abs/2402.14964

Pairing enhancement through the photography of the intermediate nucleus spectrum in a two-nucleon transfer process
While forming an ($A$+2) nucleus from a nucleus $A$ via a two-neutron transfer reaction, the constructive interference of the many possible reaction channels favors significant pairing enhancement through the continuum of the intermediate ($A$+1) nucleus [Phys. Lett. B 834, 137413 (2022)]. I analyse this situation in more detail, from the point of view of a varying pairing field leading to the formation of ($A$+2) nucleus $^6$He, described as housing two-neutrons in orbitals of $^5$He. The natu…

Interference patterns of propagating spin wave in spin Hall oscillator arrays
Mohammad Haidar
https://arxiv.org/abs/2403.15060 https://

Interference patterns of propagating spin wave in spin Hall oscillator arrays
In this study, we discuss the observation of spin wave interference generated by magnetic oscillators. We employ micromagnetic simulations for two coherent spin Hall nanowire oscillators positioned nearby, horizontally or vertically. The two nanowires produce circular waves with short wavelengths on the order of 100 nm, which interfere with each other. In the horizontal configuration, the spin waves exhibit constructive and destructive fringes, indicating amplification or cancellation of the am…

This https://arxiv.org/abs/2309.12958 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A note on complex plane curve singularities up to diffeomorphism and their rigidity
We prove that, if two germs of plane curves $(C,0)$ and $(C',0)$ with at least one singular branch are equivalent by a (real) smooth diffeomorphism, then $C$ is complex isomorphic to $C'$ or to $\overline{C'}$. A similar result was shown by Ephraim for irreducible hypersurfaces before, but his proof is not constructive. Indeed, we show that the complex isomorphism is given by the Taylor series of the diffeomorphism. We also prove an analogous result for the case of non-irreducible hypersurfaces…

Number Theory in OSCAR
Claus Fieker, Tommy Hofmann
https://arxiv.org/abs/2404.06858 https://arxiv.org/pdf/2404.06858

Number Theory in OSCAR
We give a brief introduction to computational algebraic number theory in OSCAR. Our main focus is on number fields, rings of integers and their invariants. After recalling some classical results and their constructive counterparts, we showcase the functionality in two examples related to the investigation of the Cohen-Lenstra heuristic for quadratic fields and the Galois module structure of rings of integers.

Safety-Critical Control for Autonomous Systems: Control Barrier Functions via Reduced-Order Models
Max H. Cohen, Tamas G. Molnar, Aaron D. Ames
https://arxiv.org/abs/2403.09865

Safety-Critical Control for Autonomous Systems: Control Barrier Functions via Reduced-Order Models
Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by high-dimensional nonlinear dynamics, which presents challenges for model-based safety-critical control design. Motivated by the success of reduced-order models in robotics, this paper presents a tutorial on constructive safety-critical control via reduced-order models and control barrier functions (CBFs). To this end, we provide a unified formulation of techniques in the literature that share a…

This https://arxiv.org/abs/2204.10354 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Constructive Proof that Many Groups with Non-Torsion 2-Cohomology are Not Matricially Stable
A discrete group is matricially stable if every function from the group to a complex unitary group that is "almost multiplicative" in the point-operator norm topology is "close" to a genuine unitary representation. It follows from a recent result due to Dadarlat that all amenable, groups with non-torsion integral 2-cohomology are not matricially stable, but the proof does not lead to explicit examples of asymptotic representations that are not perturbable to genuine representations. The purpose…

This https://arxiv.org/abs/2011.03619 has been replaced.
link: https://scholar.google.com/scholar?q=a

Algorithmic Extensions of Dirac's Theorem
In 1952, Dirac proved the following theorem about long cycles in graphs with large minimum vertex degrees: Every $n$-vertex $2$-connected graph $G$ with minimum vertex degree $δ\geq 2$ contains a cycle with at least $\min\{2δ,n\}$ vertices. In particular, if $δ\geq n/2$, then $G$ is Hamiltonian. The proof of Dirac's theorem is constructive, and it yields an algorithm computing the corresponding cycle in polynomial time. The combinatorial bound of Dirac's theorem is tight in the following sen…

The 2D Gray-Scott system of equations: constructive proofs of existence of localized stationary patterns
Matthieu Cadiot, Dominic Blanco
https://arxiv.org/abs/2404.08529

The 2D Gray-Scott system of equations: constructive proofs of existence of localized stationary patterns
In this article, we develop a method to perform constructive proofs of existence of smooth planar localized patterns in the Gray-Scott model. Specifically, we construct a natural Hilbert space $H^l$ for the study of systems of autonomous semi-linear PDEs, on which products and differential operators are well-defined. Then, given an approximate solution $\mathbf{u}_0$, we derive a Newton-Kantorovich approach based on the construction of an approximate inverse of the linearization around $\mathbf…

Partitioning the projective plane to two incidence-rich parts
Zolt\'an L\'or\'ant Nagy
https://arxiv.org/abs/2403.13734 https://

Partitioning the projective plane to two incidence-rich parts
An internal or friendly partition of a vertex set $V(G)$ of a graph $G$ is a partition to two nonempty sets $A\cup B$ such that every vertex has at least as many neighbours in its own class as in the other one. Motivated by Diwan's existence proof on internal partitions of graphs with high girth, we give constructive proofs for the existence of internal partitions in the incidence graph of projective planes and discuss its geometric properties. In addition, we determine exactly the maximum poss…

This https://arxiv.org/abs/1903.08945 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Note on OTM-Realizability and Constructive Set Theories
We define an ordinalized version of Kleene's realizability interpretation of intuitionistic logic by replacing Turing machines with Koepke's ordinal Turing machines (OTMs), thus obtaining a notion of realizability applying to arbitrary statements in the language of set theory. We observe that every instance of the axioms of intuitionistic first-order logic are OTM-realizable and consider the question which axioms of Friedman's Intuitionistic Set Theory (IZF) and Aczel's Constructive Set Theory …

A note on spectral theory of integral-functional Volterra operators
Denis Sidorov
https://arxiv.org/abs/2404.07041 https://arxiv.org/…

A note on spectral theory of integral-functional Volterra operators
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem has been established, outlining a procedure for determining the eigenvalues and eigenfunctions of these operators. Based on this foundation, an analytical approach for generating solutions to a Volterra-type integro-functional inhomogeneous equation is proposed.

Edge-wave phase-shifts versus normal-mode phase-tilts in an Eady problem with a sloping boundary
Julian Mak, Nili Harnik, Eyal Heifetz, Gautam Kumar, Ellie Q. Y. Ong
https://arxiv.org/abs/2404.12417

Edge-wave phase-shifts versus normal-mode phase-tilts in an Eady problem with a sloping boundary
One mechanistic interpretation of baroclinic instability is that of mutual constructive interference of Rossby edge-waves. While the two edge-waves and their relative phase-shifts are invoked as part of the mechanistic interpretation, the phase-tilts of the related normal modes are often presented instead. Here we highlight the differences between edge-wave phase-shifts and normal-mode phase-tilts, in the context of an Eady problem modified by the presence of a sloping boundary. We argue and pr…

De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application
Martin Hanik, Esfandiar Nava-Yazdani, Christoph von Tycowicz
https://arxiv.org/abs/2402.07550

De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application
For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design and has found a wide range of applications in fields such as scientific computing, and discrete geometry to name but a few. With increasing interest in nonlinear data science, its constructive approach has been shown to provide a principled way to generalize parametric smooth curves to manifolds. These curves have found remarkable new applications in the analysis of parameter-dependen…

This https://arxiv.org/abs/2309.05877 has been replaced.
initial toot: https://mastoxiv.page/@…

Choosing restart strategy at partial knowledge of process statistics
Optimization of a random processes by restart is a subject of active theoretical research in statistical physics and has long found practical application in computer science. Meanwhile, one of the key issues remains largely unsolved: when should we restart a process whose detailed statistics are unknown to ensure that our intervention will improve performance? Addressing this query here we propose several constructive criteria for the effectiveness of various protocols of non-instantaneous rest…

On the spin interface distribution for non-integrable variants of the two-dimensional Ising model
Rafael L. Greenblatt, Eveliina Peltola
https://arxiv.org/abs/2404.12375

On the spin interface distribution for non-integrable variants of the two-dimensional Ising model
We construct a martingale observable related to the spin interface for a class of non-integrable variants of the two-dimensional Ising model and express it in terms of Grassmann integrals. Under a conjecture about the scaling limit of this object, which is similar to some results recently obtained using constructive renormalization group methods, this would imply that the distribution of the interface has the same scaling limit as in the integrable model, that is, the Schramm Loewner evolution …

This https://arxiv.org/abs/1903.08945 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Note on OTM-Realizability and Constructive Set Theories
We define an ordinalized version of Kleene's realizability interpretation of intuitionistic logic by replacing Turing machines with Koepke's ordinal Turing machines (OTMs), thus obtaining a notion of realizability applying to arbitrary statements in the language of set theory. We observe that every instance of the axioms of intuitionistic first-order logic are OTM-realizable and consider the question which axioms of Friedman's Intuitionistic Set Theory (IZF) and Aczel's Constructive Set Theory …

This https://arxiv.org/abs/2403.17142 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Approximation with Random Shallow ReLU Networks with Applications to Model Reference Adaptive Control
Neural networks are regularly employed in adaptive control of nonlinear systems and related methods of reinforcement learning. A common architecture uses a neural network with a single hidden layer (i.e. a shallow network), in which the weights and biases are fixed in advance and only the output layer is trained. While classical results show that there exist neural networks of this type that can approximate arbitrary continuous functions over bounded regions, they are non-constructive, and the …

This https://arxiv.org/abs/2403.14043 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Modal logic, fundamentally
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal logics via algebraic representation theorems. We begin with complete lattices $L$ equipped with an antitone operation $\neg$ sending $1$ to $0$, a completely multiplicative operation $\Box$, and a completely additive operation $\Diamond$. Such lattice expansions …

Local Intuitionistic Modal Logics and Their Calculi
Philippe Balbiani, Han Gao, \c{C}i\u{g}dem Gencer, Nicola Olivetti
https://arxiv.org/abs/2403.06772 htt…

Local Intuitionistic Modal Logics and Their Calculi
We investigate intuitionistic modal logics with locally interpreted $\square$ and $\lozenge$. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization of LIK and some of its extensions. We propose bi-nested calculi for LIK and these extensions, thus providing both a decision procedure and a procedure of finite countermodel extraction.

This https://arxiv.org/abs/2304.01047 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Dicritical foliations and semiroots of plane branches
In this work we describe dicritical foliations in $(\mathbb{C}^2,0)$ at a triple point of the resolution dual graph of an analytic plane branch $\mathcal{C}$ using its semiroots. In particular, we obtain a constructive method to present a one-parameter family $\mathcal{C}_{u}$ of separatrices for such foliations. As a by-product we relate the contact order between a special member of $\mathcal{C}_{u}$ and $\mathcal{C}$ with analytic discrete invariants of plane branches.

An efficient uniqueness theorem for overcomplete tensor decomposition
Pascal Koiran
https://arxiv.org/abs/2404.07801 https://arxiv.or…

An efficient uniqueness theorem for overcomplete tensor decomposition
We give a new, constructive uniqueness theorem for tensor decomposition. It applies to order 3 tensors of format $n \times n \times p$ and can prove uniqueness of decomposition for generic tensors up to rank $r=4n/3$ as soon as $p \geq 4$. One major advantage over Kruskal's uniqueness theorem is that our theorem has an algorithmic proof, and the resulting algorithm is efficient. Like the uniqueness theorem, it applies in the range $n \leq r \leq 4n/3$. As a result, we obtain the first efficient…

This https://arxiv.org/abs/2312.10199 has been replaced.
link: https://scholar.google.com/scholar?q=a

Automatic nonlinear MPC approximation with closed-loop guarantees
Safety guarantees are vital in many control applications, such as robotics. Model predictive control (MPC) provides a constructive framework for controlling safety-critical systems, but is limited by its computational complexity. We address this problem by presenting a novel algorithm that automatically computes an explicit approximation to nonlinear MPC schemes while retaining closed-loop guarantees. Specifically, the problem can be reduced to a function approximation problem, which we then ta…

Complex saddles of the Veneziano amplitude
Takuya Yoda
https://arxiv.org/abs/2402.06153 https://arxiv.org/pdf/2402.06153

Complex saddles of the Veneziano amplitude
Saddle point approximation is a useful method to explore high energy asymptotic behaviors of string scattering amplitudes. We show that, even at tree-level, there are infinitely many complex saddles contributing to string scattering amplitudes, and that the complex saddles reproduce their appropriate poles and zeros. Each complex saddle is interpreted as a semi-classical path of a string in Lorentzian signature. The poles and zeros of the Veneziano amplitude are understood as constructive or de…

This https://arxiv.org/abs/2306.12713 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A constructive solution to the Oberwolfach Problem with a large cycle
For every $2$-regular graph $F$ of order $v$, the Oberwolfach problem $OP(F)$ asks whether there is a $2$-factorization of $K_v$ ($v$ odd) or $K_v$ minus a $1$-factor ($v$ even) into copies of $F$. Posed by Ringel in 1967 and extensively studied ever since, this problem is still open. In this paper we construct solutions to $OP(F)$ whenever $F$ contains a cycle of length greater than an explicit lower bound. Our constructions combine the amalgamation-detachment technique with methods aimed at b…

The Bayes Principle and Segal Axioms for $P(\phi)_2$, with application to Periodic Covers
Jiasheng Lin
https://arxiv.org/abs/2403.12804 https://

The Bayes Principle and Segal Axioms for $P(ϕ)_2$, with application to Periodic Covers
The goal of the present paper is to reconcile the so-called $P(ϕ)_2$ model from classical constructive quantum field theory (CQFT) with (metric version of) geometric and categorical axioms proposed by G. Segal \cite{Segal} in the 90's, in showing that the $P(ϕ)_2$ model satisfies these axioms, appropriately adjusted. The approach is based on previous works of Dimock arXiv:math-ph/0305017 and Pickrell arXiv:math-ph/0702077, while we give a new proof to a key step using what we call ``the Bayes…

Formal deformations of modular forms and multiple L-values
Adam Keilthy, Martin Raum
https://arxiv.org/abs/2404.03519 https://arxiv.o…

Formal deformations of modular forms and multiple L-values
We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leveraging cohomological vanishing results, we prove the existence and essential uniqueness of deformations, which we make constructive via established Lie algebraic arguments and a notion of formal logarithmic deformations. Further, we construct a canonical and a totally holomorphic canonical universal family of deformation…

Travelling waves in an ensemble of excitable oscillators: the interplay of memristive coupling and noise
Ivan A. Korneev, Ibadulla R. Ramazanov, Andrei V. Slepnev, Tatiana E. Vadivasova, Vladimir V. Semenov
https://arxiv.org/abs/2404.14147

Travelling waves in an ensemble of excitable oscillators: the interplay of memristive coupling and noise
Using methods of numerical simulation, we demonstrate the constructive role of memristive coupling in the context of the travelling waves formation and robustness in an ensemble of excitable oscillators described by the FitzHugh-Nagumo neuron model. First, the revealed aspects of the memristive coupling action are shown on an example of the deterministic model where the memristive properties of the coupling elements provide for achieving travelling waves at lower coupling strength as compared t…

Strong Priority and Determinacy in Timed CCS
Luigi Liquori, Michael Mendler
https://arxiv.org/abs/2403.04618 https://arxiv.org/pdf/24…

Strong Priority and Determinacy in Timed CCS
Building on the classical theory of process algebra with priorities, we identify a new scheduling mechanism, called "sequentially constructive reduction" which is designed to capture the essence of synchronous programming. The distinctive property of this evaluation strategy is to achieve determinism-by-construction for multi-cast concurrent communication. In particular, it permits us to model shared memory multi-threading with reaction to absence as it lies at the core of the programming langu…

This https://arxiv.org/abs/2401.08814 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Inviscid Burgers as a degenerate elliptic problem
We demonstrate the feasibility of a scheme to obtain approximate weak solutions to the (inviscid) Burgers equation in conservation and Hamilton-Jacobi form, treated as degenerate elliptic problems. We show different variants recover non-unique weak solutions as appropriate, and also specific constructive approaches to recover the corresponding entropy solutions.

This https://arxiv.org/abs/2308.06789 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Wand/set theories: A realization of Conway's mathematicians' liberation movement, with an application to Church's set theory with a universal set
Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive way of fleshing out this idea is synonymous w…

Formal deformations of modular forms and multiple L-values
Adam Keilthy, Martin Raum
https://arxiv.org/abs/2404.03519 https://arxiv.o…

Formal deformations of modular forms and multiple L-values
We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leveraging cohomological vanishing results, we prove the existence and essential uniqueness of deformations, which we make constructive via established Lie algebraic arguments and a notion of formal logarithmic deformations. Further, we construct a canonical and a totally holomorphic canonical universal family of deformation…

Modal logic, fundamentally
Wesley H. Holliday
https://arxiv.org/abs/2403.14043 https://arxiv.org/pdf/2403.14043

Modal logic, fundamentally
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal logics via algebraic representation theorems. We begin with complete lattices $L$ equipped with an antitone operation $\neg$ sending $1$ to $0$, a completely multiplicative operation $\Box$, and a completely additive operation $\Diamond$. Such lattice expansions …

This https://arxiv.org/abs/2402.19426 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Lévy noise-induced coherence resonance: numerical study versus experiment
Using the FitzHugh-Nagumo system in the excitable regime, we investigate the influence of the L{é}vy noise properties on the effect of coherence resonance. In particular, we demonstrate that the L{é}vy noise can be a constructive or destructive factor providing for enhancement or suppression of noise-induced coherence. We show that the positive or negative role of the L{é}vy noise impact is dictated by the noise stability index and skewness parameter. The correlation time and the deviation o…

Modal reduction principles: a parametric shift to graphs
Willem Conradie, Krishna Manoorkar, Alessandra Palmigiano, Mattia Panettiere
https://arxiv.org/abs/2403.14026

Modal reduction principles: a parametric shift to graphs
Graph-based frames have been introduced as a logical framework which internalizes an inherent boundary to knowability. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalizing Pawlak's rough set theory to a setting in which inherent limits to knowability need to be considered. Technically, the present paper establishes syst…

This https://arxiv.org/abs/2404.02843 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Characterization of Matrices Satisfying the Reverse Order Law for the Moore-Penrose Pseudoinverse
We give a constructive characterization of matrices satisfying the reverse-order law for the Moore--Penrose pseudoinverse. In particular, for a given matrix $A$ we construct another matrix $B$, of arbitrary compatible size and chosen rank, in terms of the right singular vectors of $A$, such that the reverse order law for $AB$ is satisfied. Moreover, we show that any matrix satisfying this law comes from a similar construction. As a consequence, several equivalent conditions to $B^+ A^+$ being a…

Canonical Temperature Control by Molecular Dynamics
William Graham Hoover, Carol Griswold Hoover
https://arxiv.org/abs/2404.05731 https://

Canonical Temperature Control by Molecular Dynamics
"Pedagogical derivations for Nosé's dynamics can be developed in two different ways, (i) by starting with a temperature-dependent Hamiltonian in which the variable $s$ scales the time or the mass, or (ii) by requiring that the equations of motion generate the canonical distribution including a Gaussian distribution in the friction coefficient $ζ$. Nosé's papers follow the former approach. Because the latter approach is not only constructive and simple, but also can be generalized to other fo…

Lewis and Brouwer meet Strong L\"ob
Albert Visser, Tadeusz Litak
https://arxiv.org/abs/2404.11969 https://arxiv.org/pdf/2404.119…

Lewis and Brouwer meet Strong Löb
We study the principle phi implies box phi, known as `Strength' or `the Completeness Principle', over the constructive version of Löb's Logic. We consider this principle both for the modal language with the necessity operator and for the modal language with the Lewis arrow, where Löb's Logic is suitably adapted. Central insights of provability logic, like the de Jongh-Sambin Theorem and the de Jongh-Sambin-Bernardi Theorem, take a simple form in the presence of Strength. We present these si…

This https://arxiv.org/abs/2312.00017 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A constructive approach for investigating the stability of incommensurate fractional differential systems
This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary and sufficient to ensure the stability of such systems. Next, from the fractional-order pseudospectrum definition proposed by Šanca et al., we formulate the concept of a rational approximation for the fractional spectrum of a noncommensurate fractional system…

The Dirichlet-Neumann Operator for Taylor's Cone
Yucong Huang, Aram Karakhanyan
https://arxiv.org/abs/2402.07005 https://arxiv.or…

The Dirichlet-Neumann Operator for Taylor's Cone
The aim of this paper is to analyse the Dirichlet-Neumann operator in axially symmetric conical domains. We provide a constructive treatment of the generic singularity at the vertex by using a new coordinate system that maps the conical domain to a strip. Building upon the paradifferential theory, we then establish our main Sobolev estimates. We also find the shape derivative, the linearization formula, and the cancellation property for the Dirichlet-Neumann operator. Our results can be viewed …