Tootfinder

In an election year partially defined by Gen Z’s exhaustion with politics, #Joe #Vogel is energized by it.
At 27 years old, the Democrat became the youngest Maryland state delegate in history.
He won his legislative seat in 2022, replacing a 16-year incumbent who retired.
Now, Vogel has his eyes set on Capitol…

Inside a Gen Z campaign to shake up Congress
Joe Vogel is running in the Democratic primary for a competitive district in Maryland. At 27 years old, he's aiming to be the second Gen Z member of Congress.

Trump's claims that immigrants are driving a surge in murders is ... just the usual racist libel.
https://www.nbcnews.com/politics/2024-election/trumps-claims-migrant-crime-wave-are-not-supported-natio…

Patriots' Jerod Mayo: 'Our legacy will be defined by' Drake Maye; rookie to compete with Jacoby Brissett at QB

https://www.cbssports…

Patriots' Jerod Mayo: 'Our legacy will be defined by' Drake Maye; rookie to compete with Jacoby Brissett at QB
Look out for a summer competition under center

If you use a parameter object in JavaScript, even if you specify its shape using JSDoc, you’ll only get errors if required properties are missing; not if there are extra properties provided.
e.g.,
```js
class A {
/**
@param {{
id:string
}} params
*/
constructor (params) {
Object.assign(this, params)
}
}
// Error:
new A({})
// No error:
new A({id: 'x', foo:'bar'})

Is it possible to restrict TypeScript object to contain only properties defined by its class?
Here is my code async getAll(): Promise { return await dbQuery(); // dbQuery returns User[] } class User { id: number; name: string; } class GetAllUserData{ ...

A Class of Numerical Semigroups Defined by Kunz and Waldo
Srishti Singh, Hema Srinivasan
https://arxiv.org/abs/2405.00331 https://arx…

A Class of Numerical Semigroups Defined by Kunz and Waldo
In this paper, we explore a class of numerical semigroups initiated by Kunz and Waldi containing two coprime numbers $p < q$, which we call KW semigroups. We characterize KW numerical semigroups by their principal matrices. We present a necessary and sufficient criterion for a matrix to be the principal matrix of a KW semigroup. An explicit description of the minimal resolutions of numerical semigroups in the same class with small embedding dimensions 3 and 4 is given. We give a generalization …

#Trump's claims of a migrant crime wave are not supported by national data
https://www.nbcnews.com/politics/2024-elec

Trump's claims of a migrant crime wave are not supported by national data
When Donald Trump speaks at the southern border in Texas on Thursday, you can expect to hear him talk about “migrant crime” a criminal category he has coined and defined as a terrifying binge of criminal activity committed by undocumented immigrants spreading across the country.

Das Set von Mars Kumari gestern war auch sehr fein, übrigens. #sound
[Überhaupt: Vier Sets um wohlfeile 25 US$, und es gab recht anregende Mezcalito-Cocktails an der Bar.]
https://marskumari.bandcamp.com/

mars kumari
When Jacques Derrida defined the lingering Marxism of late-Capitalist society as hauntological, mashing together the words haunting and ontology, he couldn’t have imagined what the era might sound like. Mars Kumari captures the grief and grit of loss we all feel now, haunted as we are by what was here and is now missing." -Roy Christopher Deadverse Bruiser Brigade

John Barth, a Novelist Who Found Possibility in a ‘Used-Up’ Form - The New York Times
https://www.nytimes.com/2024/04/02/books/review/john-barth-appreciation.html

John Barth, a Novelist Who Found Possibility in a ‘Used-Up’ Form
By merrily using fiction to dissect itself, he was at the vanguard of a movement that defined a postwar American style.

This https://arxiv.org/abs/2312.04352 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Gravitational Multipoles in Five Dimensions
We define gravitational mass and current multipoles for five-dimensional, stationary, and asymptotically flat vacuum metrics. We do this by generalizing Thorne's asymptotically Cartesian and mass-centered (ACMC) coordinate formalism to five dimensions, and prove that the multipoles defined in this way are unambiguously well-defined. Further, these two towers of multipole tensors, in the case of biaxial symmetry, reduce to a tower of mass multipoles $M_\ell$, and two separate towers of current o…

Polynomial Divided Difference Operators Satisfying the Braid Relations
Shaul Zemel
https://arxiv.org/abs/2404.19395 https://arxiv.org…

Polynomial Divided Difference Operators Satisfying the Braid Relations
Many interesting families of polynomials are indexed by permutations or related objects, and are defined by applying divided difference operators, modified by polynomials, on some initial base case. The fact that these constructions produce well-defined polynomials is based on the applied modified divided difference operators satisfying the braid relations. We thus determine all the families of polynomial divided difference operators that satisfy the braid relations.

This https://arxiv.org/abs/2310.19518 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the splitting of weak nearly cosymplectic manifolds
Weak almost contact manifolds, i.e., the linear complex structure on the contact distribution is approximated by a nonsingular skew-symmetric tensor, defined by the author and R. Wolak (2022), allowed a new look at the theory of contact manifolds. This article studies the curvature and topology of new structures of this type, called the weak nearly cosymplectic structure and weak nearly Kähler structure. We find conditions under which weak nearly cosymplectic manifolds become Riemannian produc…

CARLOS: An Open, Modular, and Scalable Simulation Framework for the Development and Testing of Software for C-ITS
Christian Geller, Benedikt Haas, Amarin Kloeker, Jona Hermens, Bastian Lampe, Lutz Eckstein
https://arxiv.org/abs/2404.01836

CARLOS: An Open, Modular, and Scalable Simulation Framework for the Development and Testing of Software for C-ITS
Future mobility systems and their components are increasingly defined by their software. The complexity of these cooperative intelligent transport systems (C-ITS) and the everchanging requirements posed at the software require continual software updates. The dynamic nature of the system and the practically innumerable scenarios in which different software components work together necessitate efficient and automated development and testing procedures that use simulations as one core methodology.…

🎉 Congrats to the #OpenTofu team on releasing v1.7.0! This is a big deal. It includes new, long-requested functionality mostly ignored by the #Terraform project for years: end-to-end state #encryption.

OpenTofu 1.7.0 is out with State Encryption, Dynamic Provider-Defined Functions, and more | OpenTofu
OpenTofu 1.7.0 is now available with full state encryption, dynamic provider-defined functions, the removed and loopable import blocks, new migration guides, and much more.

The Nucleus of a Compact Lie Group, and Support of Singularity Categories
Thomas Peirce
https://arxiv.org/abs/2405.00457 https://arxi…

The Nucleus of a Compact Lie Group, and Support of Singularity Categories
In this paper we adapt the notion of the nucleus defined by Benson, Carlson, and Robinson to compact Lie groups in non-modular characteristic. We show that it describes the singularities of the projective scheme of the cohomology of its classifying space. A notion of support for singularity categories of ring spectra (in the sense of Greenlees and Stevenson) is established, and is shown to be precisely the nucleus in this case, consistent with a conjecture of Benson and Greenlees for finite gro…

Effective Categorical Enumerative Invariants
Andrei Caldararu, Junwu Tu
https://arxiv.org/abs/2404.01499 https://arxiv.org/pdf/2404.0…

Effective Categorical Enumerative Invariants
We introduce enumerative invariants $F_{g,n}$ $(g\geq0$, $n \geq 1)$ associated to a cyclic $A_\infty$ algebra and a splitting of its non-commutative Hodge filtration. These invariants are defined by explicitly computable Feynman sums, and encode the same information as Costello's partition function of the corresponding field theory. Our invariants are stable under Morita equivalence, and therefore can be associated to a Calabi-Yau category with splitting data. This justifies the name categor…

Here's an optimist:
"Britain has the potential to become an envied European economic and social model."
The UK is trapped in a cycle of political, social and financial turmoil. But there is a way out… https://www.theguardian.com…

MaRDIFlow: A CSE workflow framework for abstracting meta-data from FAIR computational experiments
Pavan L. Veluvali, Jan Heiland, Peter Benner
https://arxiv.org/abs/2405.00028

MaRDIFlow: A CSE workflow framework for abstracting meta-data from FAIR computational experiments
Numerical algorithms and computational tools are instrumental in navigating and addressing complex simulation and data processing tasks. The exponential growth of metadata and parameter-driven simulations has led to an increasing demand for automated workflows that can replicate computational experiments across platforms. In general, a computational workflow is defined as a sequential description for accomplishing a scientific objective, often described by tasks and their associated data depend…

This https://arxiv.org/abs/2404.01286 has been replaced.
link: https://scholar.google.com/scholar?q=a

Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport
A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol that drives a nonequilibrium system between two thermodynamic states in the slow-driving limit is given by a geodesic of the friction tensor, a Riemannian metric defined on control space. For overdamped dynamics in arbitrary dimensions, we demonstrate that thermodynamic geometry is equivalent to $L^2$ optimal transport geometry defined on the space of equilibrium distributions corresponding to the control …

This https://arxiv.org/abs/2403.10560 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Holographic Phase Retrieval via Wirtinger Flow: Cartesian Form with Auxiliary Amplitude
We propose a new gradient method for holography, where a phase-only hologram is parameterized by not only the phase but also amplitude. The key idea of our approach is the formulation of a phase-only hologram using an auxiliary amplitude. We optimize the parameters using the so-called Wirtinger flow algorithm in the Cartesian domain, which is a gradient method defined on the basis of the Wirtinger calculus. At the early stage of optimization, each element of the hologram exists inside a complex…

Regularity results for almost-minimizers of anisotropic free interface problem with H\"older dependence on the position
Luca Esposito, Lorenzo Lamberti, Giovanni Pisante
https://arxiv.org/abs/2404.02086

Regularity results for almost-minimizers of anisotropic free interface problem with Hölder dependence on the position
We establish regularity results for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behaviour and is defined by means of an ellipsoidal density that is Hölder continuous with respect to the position variable.

This https://arxiv.org/abs/2403.16752 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hep…

Action of the axial $U(1)$ non-invertible symmetry on the 't~Hooft line operator: A lattice gauge theory study
We study how the symmetry operator of the axial $U(1)$ non-invertible symmetry acts on the 't~Hooft line operator in the $U(1)$ gauge theory by employing the modified Villain-type lattice formulation. We model the axial anomaly by a compact scalar boson, the ``QED axion''. For the gauge invariance, the simple 't~Hooft line operator, which is defined by a line integral of the dual $U(1)$ gauge potential, must be ``dressed'' by the scalar and $U(1)$ gauge fields. The anomalous Ward--Takahashi ide…

This https://arxiv.org/abs/2108.03018 has been replaced.
link: https://scholar.google.com/scholar?q=a

Conditional Separation as a Binary Relation. A Coq Assisted Proof
The concept of d-separation holds a pivotal role in causality theory, serving as a fundamental tool for deriving conditional independence properties from causal graphs. Pearl defined the d-separation of two subsets conditionally on a third one. In this study, we present a novel perspective by showing i) how the d-separation can be extended beyond acyclic graphs, possibly infinite, and ii) how it can be expressed and characterized as a binary relation between vertices. Compared to the typ…

This https://arxiv.org/abs/2311.02387 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A note on a Conjecture of Gao and Zhuang for groups of order $27$
The small Davenport constant ${\mathsf{d}}(G)$ of a finite group $G$ is defined to be the maximal length of a sequence over $G$ which has no non-trivial product-one subsequence. In this paper, we prove that ${\mathsf{d}}(G) = 6$ for the non-abelian group of order $27$ and exponent $3$ and thereby establish a conjecture by Gao and Zhuang for this group.

Invariant Checking for SMT-based Systems with Quantifiers
Gianluca Redondi, Alessandro Cimatti, Alberto Griggio, Kenneth McMillan
https://arxiv.org/abs/2402.19028

Invariant Checking for SMT-based Systems with Quantifiers
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort (finite, but unbounded) to an interpreted sort, such as the the integers under the theory of linear arithmetic. This formalism is very expressive and can be used for modeling parameterized systems, array-manipulating programs, and more. We propose two algorithms fo…

This https://arxiv.org/abs/2005.08681 has been replaced.
link: https://scholar.google.com/scholar?q=a

Enumerative Geometry of Del Pezzo Surfaces
We prove an equivalence between the superpotential defined via tropical geometry and Lagrangian Floer theory for special Lagrangian torus fibres in del Pezzo surfaces constructed by Collins-Jacob-Lin. We also include some explicit calculations for the projective plane, which confirm some folklore conjecture in this case.

This https://arxiv.org/abs/2402.01847 has been replaced.
link: https://scholar.google.com/scholar?q=a

Relativity of the event: examples in JT gravity and linearized GR
Observables in quantum gravity are famously defined asymptotically, at the boundary of AdS or Minkowski spaces. However, by gauge fixing a coordinate system or suitably dressing the field operators, an approximate, "quasi-local" approach is also possible, that can give account of the measurements performed by a set of observers living inside the spacetime. In particular, one can attach spatial coordinates to the worldlines of these observers and use their proper times as a time coordinate. Here…

Strength and Sensitivity of Land-Atmosphere Interaction
Jun Yin
https://arxiv.org/abs/2405.01287 https://arxiv.org/pdf/2405.01287

Strength and Sensitivity of Land-Atmosphere Interaction
The land-atmosphere coupling strength has been defined as the percentage of precipitation variability explained by the variation of soil moisture in the Global Land-Atmosphere Coupling Experiment (GLACE). While it is useful to identify global hotspots of land-atmosphere interaction, this coupling strength is different from coupling sensitivity, which directly quantifies how precipitation generation responds to the perturbation of soil moisture and is essential for our understanding of the globa…

This https://arxiv.org/abs/2404.07768 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

Using Letter Positional Probabilities to Assess Word Complexity
Word complexity is defined in a number of different ways. Psycholinguistic, morphological and lexical proxies are often used. Human ratings are also used. The problem here is that these proxies do not measure complexity directly, and human ratings are susceptible to subjective bias. In this study we contend that some form of 'latent complexity' can be approximated by using samples of simple and complex words. We use a sample of 'simple' words from primary school picture books and a sample of 'c…

Conformal Invariance of Clifford Monogenic Functions in the Indefinite Signature Case
Chen Liang, Matvei Libine
https://arxiv.org/abs/2404.01398 https://…

Conformal Invariance of Clifford Monogenic Functions in the Indefinite Signature Case
We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. Clifford analogues of complex holomorphic functions - called monogenic functions - are defined by means of the Dirac operators that factor a certain wave operator. One of the fundamental features of quaternionic analysis is the invariance of quaternionic analogues of holomorphic function under conformal (or Mobius) transformations. A similar invariance property is known to hold in th…

🛸 Linux can finally run your car’s safety systems and driver-assistance features
#linux

Linux is now an option for safety-minded software-defined vehicle developers
Increasingly, our cars will be controlled by a small number of powerful computers.

Spatial distribution of crystalline silicates in protoplanetary disks: How to interpret mid-infrared observations
Hyerin Jang, L. B. F. M. Waters, I. Kamp, C. P. Dullemond
https://arxiv.org/abs/2405.00375

Spatial distribution of crystalline silicates in protoplanetary disks: How to interpret mid-infrared observations
Crystalline silicates are an important tracer to the dust evolution in protoplanetary disks. In the inner disk, amorphous silicates are annealed by the high temperatures. These crystalline silicates are radially and vertically distributed in the disk. We aim to model the spatial distribution of crystalline silicate in the disk and its mid-IR spectra to study the effect on dust spectral features and to compare these to observations. We modeled a T-Tauri protoplanetary disk and defined the crysta…

Daily inspiration: "Do the wrong things for the right reasons!"- Futurist Jim Carroll
History celebrates the rule-breakers who did the wrong things for the right reasons!
Rosa Parks - she defined the push for civil rights by refusing to sit where she was told. Martin Luther King for a regular series of arrests in violation of demands that he refrain from protesting. Dick Leitsch for conducting a "sip-in" at a New York bar to challenge the prohibition against s…

Daily Inspiration: Innovation & Risk – “Do the wrong things for the right reasons!”

Pretzel monoids
Daniel Heath, Mark Kambites, N\'ora Szak\'acs
https://arxiv.org/abs/2405.00589 https://arxiv.org/pdf/2405.005…

Pretzel monoids
We introduce an interesting class of left adequate monoids which we call pretzel monoids. These, on the one hand, are monoids of birooted graphs with respect to a natural `glue-and-fold' operation, and on the other hand, are shown to be defined in the category of left adequate monoids by a natural class of presentations. They are also shown to be the free idempotent-pure expansions of right cancellative monoids, making them, in some sense, the left adequate analogues of Margolis-Meakin expansio…

This https://arxiv.org/abs/2311.05413 has been replaced.
initial toot: https://mastoxiv.page/@a…

Strain fluctuations unlock ferroelectricity in wurtzites
Ferroelectrics are of practical interest for non-volatile data storage due to their reorientable, crystallographically defined polarization. Yet efforts to integrate conventional ferroelectrics into ultrathin memories have been frustrated by film-thickness limitations, which impede polarization reversal under low voltage. Wurtzite materials, including magnesium-substituted zinc oxide (Zn,Mg)O, have been shown to exhibit scalable ferroelectricity as thin films. In this work, we explain the origi…

This https://arxiv.org/abs/2308.10812 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On countable isotypic structures
We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with countable underlying sets: totally ordered sets, fields, and groups. This answers an old question by B. Plotkin for groups.

This https://arxiv.org/abs/2305.02574 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Elementary Proof of the Inequality $χ\leq χ^*$ for Conditional Free Entropy
Through the study of large deviations theory for matrix Brownian motion, Biane-Capitaine-Guionnet proved the inequality $χ(X) \leq χ^*(X)$ that relates two analogs of entropy in free probability defined by Voiculescu. We give a new proof of $χ\leq χ^*$ that is elementary in the sense that it does not rely on stochastic differential equations and large deviation theory. Moreover, we generalize the result to conditional microstates and non-microstates free entropy.

Scalar perturbations from inflation in the presence of gauge fields
R. Durrer, R. von Eckardstein, Deepen Garg, K. Schmitz, O. Sobol, S. Vilchinskii
https://arxiv.org/abs/2404.19694

Scalar perturbations from inflation in the presence of gauge fields
We study how Abelian-gauge-field production during inflation affects scalar perturbations in the case when the gauge field interacts with the inflaton directly (by means of generic kinetic and axial couplings) and via gravity. The homogeneous background solution is defined by self-consistently taking into account the backreaction of the gauge field on the evolution of the inflaton and the scale factor. For the perturbations on top of this background, all possible scalar contributions coming fro…

This https://arxiv.org/abs/2305.08643 has been replaced.
link: https://scholar.google.com/scholar?q=a

Quadratic Programming-based Reference Spreading Control for Dual-Arm Robotic Manipulation with Planned Simultaneous Impacts
With the aim of further enabling the exploitation of intentional impacts in robotic manipulation, a control framework is presented that directly tackles the challenges posed by tracking control of robotic manipulators that are tasked to perform nominally simultaneous impacts. This framework is an extension of the reference spreading control framework, in which overlapping ante- and post-impact references that are consistent with impact dynamics are defined. In this work, such a reference is con…

Adaptive Gradient Enhanced Gaussian Process Surrogates for Inverse Problems
Phillip Semler, Martin Weiser
https://arxiv.org/abs/2404.01864 https://<…

Adaptive Gradient Enhanced Gaussian Process Surrogates for Inverse Problems
Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a fully adaptive greedy approach to the computational design of experiments problem using gradient-enhanced Gaussian process regression as surrogates. Designs are incrementally defined by solving an optimization problem for accuracy given a certain computational …

Demonstration of system-bath physics on gate-based quantum computer
Pascal Stadler, Matteo Lodi, Andisheh Khedri, Rolando Reiner, Kirsten Bark, Nicolas Vogt, Michael Marthaler, Juha Lepp\"akangas
https://arxiv.org/abs/2404.18828

Demonstration of system-bath physics on gate-based quantum computer
We demonstrate algorithmic cooling on IBM-Q devices. We utilize inherent qubit noise to simulate the equilibration of an interacting spin system towards its ground state, when coupled to a dissipative auxiliary-spin bath. The steady-state correlations in the system are defined by the system Hamiltonian and are stable as long as the algorithm can be executed. In particular, we demonstrate the relaxation of system spins to ferromagnetic and antiferromagnetic ordering, controlled by the definition…

This https://arxiv.org/abs/1808.09991 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Weyl law for algebraic tori
We give an asymptotic evaluation for the number of automorphic characters of an algebraic torus $T$ with bounded analytic conductor. The analytic conductor which we use is defined via the local Langlands correspondence for tori by choosing a finite dimensional complex algebraic representation of the $L$-group of $T$. Our results therefore fit into a general framework of counting automorphic representations on reductive groups by analytic conductor.

My god, people don’t stop mentioning Alonso’s age… come on! Give the guy some respect! He can’t be defined by his age. He’s proven fit, so get over it.
#F1

The Nucleus of a Compact Lie Group, and Support of Singularity Categories
Thomas Peirce
https://arxiv.org/abs/2405.00457 https://arxi…

The Nucleus of a Compact Lie Group, and Support of Singularity Categories
In this paper we adapt the notion of the nucleus defined by Benson, Carlson, and Robinson to compact Lie groups in non-modular characteristic. We show that it describes the singularities of the projective scheme of the cohomology of its classifying space. A notion of support for singularity categories of ring spectra (in the sense of Greenlees and Stevenson) is established, and is shown to be precisely the nucleus in this case, consistent with a conjecture of Benson and Greenlees for finite gro…

This https://arxiv.org/abs/2309.13633 has been replaced.
link: https://scholar.google.com/scholar?q=a

EvalLM: Interactive Evaluation of Large Language Model Prompts on User-Defined Criteria
By simply composing prompts, developers can prototype novel generative applications with Large Language Models (LLMs). To refine prototypes into products, however, developers must iteratively revise prompts by evaluating outputs to diagnose weaknesses. Formative interviews (N=8) revealed that developers invest significant effort in manually evaluating outputs as they assess context-specific and subjective criteria. We present EvalLM, an interactive system for iteratively refining prompts by eva…

Effective Categorical Enumerative Invariants
Andrei Caldararu, Junwu Tu
https://arxiv.org/abs/2404.01499 https://arxiv.org/pdf/2404.0…

Effective Categorical Enumerative Invariants
We introduce enumerative invariants $F_{g,n}$ $(g\geq0$, $n \geq 1)$ associated to a cyclic $A_\infty$ algebra and a splitting of its non-commutative Hodge filtration. These invariants are defined by explicitly computable Feynman sums, and encode the same information as Costello's partition function of the corresponding field theory. Our invariants are stable under Morita equivalence, and therefore can be associated to a Calabi-Yau category with splitting data. This justifies the name categor…

A Python code for calculating the mean-value (Baldereschi's) point for any crystal structure
Vladan Stevanovic
https://arxiv.org/abs/2405.00925 https:/…

A Python code for calculating the mean-value (Baldereschi's) point for any crystal structure
A python code (mvp.py) is presented for computing the mean-value point (MVP) in the Brillouin zone first introduced by Baldereschi [1]. The code allows calculations of the MVP for any input crystal structure. Having MVP allows approximating the Brillouin zone integrals of relatively smooth, periodic functions defined in the reciprocal space by the value of the same function at only one, mean-value, k-point. This approximation decreases computational cost at a relatively small decrease in accura…

Weighted Catalan convolution and $(q,2)$-Fock space
Yungang Lu
https://arxiv.org/abs/2402.19447 https://arxiv.org/pdf/2402.19447

Weighted Catalan convolution and $(q,2)$-Fock space
Motivated by the study of certain combinatorial properties of $(q,2)$-Fock space, we compute explicitly a sequence driven by the Catalan's convolution and parameterized by $1+q$. As an application of this explicit form, we calculate the number of pair partitions involved in the determination of the vacuum--moments of the field operator defined on the $(q,2)$-Fock space.

This https://arxiv.org/abs/2404.12286 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Conjugate Operators of 1D-harmonic Oscillator
Conjugate operator $T$ of 1D-harmonic oscillator $N=1/2 (p^2+q^2-1)$ is defined by an operator satisfying canonical commutation relation $[N,T]=-i$ on some domain but not necessarily dense. The angle operator $T_A=1/2 (\arctan q^{-1} p+\arctan pq^{-1} )$ and Galapon operator $T_G=i \sum_{n=0}^\infty(\sum_{m\neq n}\frac{(v_m,\cdot) }{n-m}v_n)$ are examples of conjugate operators, where ${v_n}$ denotes the set of normalized eigenvectors of $N$. Let $T$ be a subset of conjugate operators of $N$. A…

It does not matter what your age is. Vigilance, scepticism, not panicking is important. Someone is out to get you and will do anything and say anything.
https://www.new…

This https://arxiv.org/abs/2402.15156 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Spacetime singularities and caustic of outgoing null hypersurfaces
In this paper, we investigate the caustic point developed by outgoing null hypersurfaces and the behavior of null curves. We analyze three cases: Future, past, and zero caustic point terminology for outgoing null hypersurfaces in the marginally bound Lemaitre-Tolman-Bondi (LTB) metric for homogenous and inhomogeneous cases defined in the present work. We show the criteria to form local and globally visible singularity in terms of the tangent on the apparent horizon curve.

Drazin Inverses in Categories
Robin Cockett, Jean-Simon Pacaud Lemay, Priyaa Varshinee Srinivasan
https://arxiv.org/abs/2402.18226 https://

Drazin Inverses in Categories
Drazin inverses are a fundamental algebraic structure which have been extensively deployed in semigroup theory and ring theory. Drazin inverses can also be defined for endomorphisms in any category. However, beyond a paper by Puystjens and Robinson from 1987, not much has been done with Drazin inverses in category theory. As such, here we provide a survey of the theory of Drazin inverses from a categorical perspective. We introduce Drazin categories, in which every endomorphism has a Drazin inv…

Smart Grids Secured By Dynamic Watermarking: How Secure?
Kate Davis, Laszlo B. Kish, Chanan Singh
https://arxiv.org/abs/2404.16849 https://

Smart Grids Secured By Dynamic Watermarking: How Secure?
Unconditional security for smart grids is defined. Cryptanalyses of the watermarked security of smart grids indicate that watermarking cannot guarantee unconditional security unless the communication within the grid system is unconditionally secure. The successful attack against the dynamically watermarked smart grid remains valid even with the presence of internal noise from the grid. An open question arises: if unconditionally authenticated secure communications within the grid, together with…

This https://arxiv.org/abs/2404.15764 has been replaced.
link: https://scholar.google.com/scholar?q=a

Assessment of the quality of a prediction
Shannon defined the mutual information between two variables. We illustrate why the true mutual information between a variable and the predictions made by a prediction algorithm is not a suitable measure of prediction quality, but the apparent Shannon mutual information (ASI) is; indeed it is the unique prediction quality measure with either of two very different lists of desirable properties, as previously shown by de Finetti and other authors. However, estimating the uncertainty of the ASI is…

Copula Approximate Bayesian Computation Using Distribution Random Forests
George Karabatsos
https://arxiv.org/abs/2402.18450 https://…

Copula Approximate Bayesian Computation Using Distribution Random Forests
This paper introduces a novel Approximate Bayesian Computation (ABC) framework for estimating the posterior distribution and the maximum likelihood estimate (MLE) of the parameters of models defined by intractable likelihood functions. This framework can describe the possibly skewed and high dimensional posterior distribution by a novel multivariate copula-based distribution, based on univariate marginal posterior distributions which can account for skewness and be accurately estimated by Distr…

Sharp embedding results and geometric inequalities for H\"{o}rmander vector fields
Hua Chen, Hong-Ge Chen, Jin-Ning Li
https://arxiv.org/abs/2404.19393 https://arxiv.org/pdf/2404.19393
arXiv:2404.19393v1 Announce Type: new
Abstract: Let $U$ be a connected open subset of $\mathbb{R}^n$, and let $X=(X_1,X_{2},\ldots,X_m)$ be a system of H\"{o}rmander vector fields defined on $U$. This paper addresses sharp embedding results and geometric inequalities in the generalized Sobolev space $\mathcal{W}_{X,0}^{k,p}(\Omega)$, where $\Omega\subset\subset U$ is a general open bounded subset of $U$. By employing Rothschild-Stein's lifting technique and saturation method, we prove the representation formula for smooth functions with compact support in $\Omega$. Combining this representation formula with weighted weak-$L^p$ estimates, we derive sharp Sobolev inequalities on $\mathcal{W}_{X,0}^{k,p}(\Omega)$, where the critical Sobolev exponent depends on the generalized M\'{e}tivier index. As applications of these sharp Sobolev inequalities, we establish the isoperimetric inequality, logarithmic Sobolev inequalities, Rellich-Kondrachov compact embedding theorem, Gagliardo-Nirenberg inequality, Nash inequality, and Moser-Trudinger inequality in the context of general H\"{o}rmander vector fields.

Identification by non-Gaussianity in structural threshold and smooth transition vector autoregressive models
Savi Virolainen
https://arxiv.org/abs/2404.19707

Identification by non-Gaussianity in structural threshold and smooth transition vector autoregressive models
Linear structural vector autoregressive models can be identified statistically without imposing restrictions on the model if the shocks are mutually independent and at most one of them is Gaussian. We show that this result extends to structural threshold and smooth transition vector autoregressive models incorporating a time-varying impact matrix defined as a weighted sum of the impact matrices of the regimes. Our empirical application studies the effects of the climate policy uncertainty shock…

Non-semisimple Crane-Yetter theory varying over the character stack
Patrick Kinnear
https://arxiv.org/abs/2404.19667 https://arxiv.org/pdf/2404.19667
arXiv:2404.19667v1 Announce Type: new
Abstract: We construct a relative version of the Crane-Yetter topological quantum field theory in four dimensions, from non-semisimple data. Our theory is defined relative to the classical $G$-gauge theory in five dimensions -- this latter theory assigns to each manifold $M$ the appropriate linearization of the moduli stack of $G$-local systems, called the character stack. Our main result is to establish a relative invertibility property for our construction. This invertibility echoes -- recovers and greatly generalizes -- the key invertibility property of the original Crane-Yetter theory which allowed it to capture the framing anomaly of the celebrated Witten-Reshetikhin-Turaev theory. In particular our invertibilty statement at the level of surfaces implies a categorical, stacky version of the unicity theorem for skein algebras; at the level of 3-manifolds it equips the character stack with a canonical line bundle. Regarded as a topological symmetry defect of classical gauge theory, our work establishes invertibility of this defect by a gauging procedure.

This https://arxiv.org/abs/2308.06760 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Diquarks and the production of charmed baryons
Utilizing a quark model characterized by parameters that effectively replicate the masses of ground state hadrons, we illustrate that $(us)$ or $(ds)$ diquarks exhibit greater compactness in comparison to $(ud)$ diquarks. Concretely, the binding energy of the $(us)$ diquark - defined as the diquark's mass minus the combined masses of its individual quarks - is found to be stronger than that of the $(ud)$ diquark. This heightened attraction present in $(us)$ diquarks could lead to enhanced produ…

Communication-Constrained STL Task Decomposition through Convex Optimization
Gregorio Marchesini, Siyuan Liu, Lars Lindemann, Dimos V. Dimarogonas
https://arxiv.org/abs/2402.17585

Communication-Constrained STL Task Decomposition through Convex Optimization
In this work, we propose a method to decompose signal temporal logic (STL) tasks for multi-agent systems subject to constraints imposed by the communication graph. Specifically, we propose to decompose tasks defined over multiple agents which require multi-hop communication, by a set of sub-tasks defined over the states of agents with 1-hop distance over the communication graph. To this end, we parameterize the predicates of the tasks to be decomposed as suitable hyper-rectangles. Then, we show…

This https://arxiv.org/abs/2402.17279 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

DiFashion: Towards Personalized Outfit Generation
The evolution of Outfit Recommendation (OR) in the realm of fashion has progressed through two distinct phases: Pre-defined Outfit Recommendation and Personalized Outfit Composition. Despite these advancements, both phases face limitations imposed by existing fashion products, hindering their effectiveness in meeting users' diverse fashion needs. The emergence of AI-generated content has paved the way for OR to overcome these constraints, demonstrating the potential for personalized outfit gene…

Optimal Communication for Classic Functions in the Coordinator Model and Beyond
Hossein Esfandiari, Praneeth Kacham, Vahab Mirrokni, David P. Woodruff, Peilin Zhong
https://arxiv.org/abs/2403.20307

Optimal Communication for Classic Functions in the Coordinator Model and Beyond
In the coordinator model of communication with $s$ servers, given an arbitrary non-negative function $f$, we study the problem of approximating the sum $\sum_{i \in [n]}f(x_i)$ up to a $1 \pm \varepsilon$ factor. Here the vector $x \in R^n$ is defined to be $x = x(1) + \cdots + x(s)$, where $x(j) \ge 0$ denotes the non-negative vector held by the $j$-th server. A special case of the problem is when $f(x) = x^k$ which corresponds to the well-studied problem of $F_k$ moment estimation in the dist…

This https://arxiv.org/abs/2108.03018 has been replaced.
link: https://scholar.google.com/scholar?q=a

Conditional Separation as a Binary Relation. A Coq Assisted Proof
The concept of d-separation holds a pivotal role in causality theory, serving as a fundamental tool for deriving conditional independence properties from causal graphs. Pearl defined the d-separation of two subsets conditionally on a third one. In this study, we present a novel perspective by showing i) how the d-separation can be extended beyond acyclic graphs, possibly infinite, and ii) how it can be expressed and characterized as a binary relation between vertices. Compared to the typ…

This https://arxiv.org/abs/2303.01738 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Variational principle for neutralized Bowen topological entropy
Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as $$B_n(x,e^{-nε})=\{y\in X: d(T^jx, T^jy)

The sentence "all men were created equal" in the US Declaration of Independence meant nothing more than the repealing of the European system of nobility, where people were ranked in a strict hierarchy defined by king edicts or by birth ("creation") rights.
And the word "men" there obviously meant only males, and only white males. To the Founders, the idea that it could include also women, slaves, and natives would have never occurred and would seem laugha…

This https://arxiv.org/abs/2305.08643 has been replaced.
link: https://scholar.google.com/scholar?q=a

Quadratic Programming-based Reference Spreading Control for Dual-Arm Robotic Manipulation with Planned Simultaneous Impacts
With the aim of further enabling the exploitation of intentional impacts in robotic manipulation, a control framework is presented that directly tackles the challenges posed by tracking control of robotic manipulators that are tasked to perform nominally simultaneous impacts. This framework is an extension of the reference spreading control framework, in which overlapping ante- and post-impact references that are consistent with impact dynamics are defined. In this work, such a reference is con…

Strength and Sensitivity of Land-Atmosphere Interaction
Jun Yin
https://arxiv.org/abs/2405.01287 https://arxiv.org/pdf/2405.01287

Strength and Sensitivity of Land-Atmosphere Interaction
The land-atmosphere coupling strength has been defined as the percentage of precipitation variability explained by the variation of soil moisture in the Global Land-Atmosphere Coupling Experiment (GLACE). While it is useful to identify global hotspots of land-atmosphere interaction, this coupling strength is different from coupling sensitivity, which directly quantifies how precipitation generation responds to the perturbation of soil moisture and is essential for our understanding of the globa…

Algebraic structures in Lagrangian Floer cohomology modelled on differential forms
Peleg Bar-Lev
https://arxiv.org/abs/2404.02020 https://

Algebraic structures in Lagrangian Floer cohomology modelled on differential forms
We define a structure of an algebra on the Lagrangian Floer cohomology of a Lagrangian submanifold over the quantum cohomology of the ambient symplectic manifold. The structure is analogous to the one defined by Biran-Cornea, but is constructed in the differential forms model. In the spirit of Ganatra and Hugtenburg, we define another such algebra structure using a closed-open map. We show that the two structures coincide. As an application, we show that the module structure for the 2-dimension…

This https://arxiv.org/abs/2307.07902 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the regularization of sequences and associated weight functions
We revisit and generalize the geometric procedure of regularizing a sequence of real numbers with respect to a so-called regularizing function. This approach was studied by S. Mandelbrojt and becomes useful and necessary when working with corresponding classes of ultradifferentiable functions defined via weight sequences and analogous weighted spaces. In this note we also study non-standard situations for the construction yielding the (log-)convex minorant of a sequence and allow a "blow-up" fo…

This https://arxiv.org/abs/2401.00574 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Exact WKB analysis for ${\cal PT}$ symmetric quantum mechanics: Study of the Ai-Bender-Sarkar conjecture
We consider exact WKB analysis to a ${\cal PT}$ symmetric quantum mechanics defined by the potential, $V(x) = ω^2 x^2 + g x^2(i x)^{\varepsilon=2}$ with $ω\in {\mathbb R}_{\ge 0}$, $g \in {\mathbb R} _{> 0}$. We in particular aim to verify a conjecture proposed by Ai-Bender-Sarkar (ABS), that pertains to a relation between $D$-dimensional ${\cal PT}$-symmetric theories and analytic continuation (AC) of Hermitian theories concerning the energy spectrum or Euclidean partition function. For the …

CyberShake Earthquake Fault Rupture Modeling and Ground Motion Simulations for the Southwest Iceland Transform Zone
Otilio Rojas, Marisol Monterrubio-Velasco, Juan E. Rodriguez, Scott Callaghan, Claudia Abril, Benedikt Holldorson, Milad Kowsari, Farnaz Bayat, Kim Olsen, Alice-Agnes Gabriel, Josep de la Puente
https://arxiv.org/a…

CyberShake Earthquake Fault Rupture Modeling and Ground Motion Simulations for the Southwest Iceland Transform Zone
CyberShake (CS) is a high-performance computing workflow for Probabilistic Seismic Hazard Assessment (PSHA) developed by the Statewide California Earthquake Center. Here, we employ CS to generate a set of 2103 fault ruptures and simulate the corresponding two horizontal velocity components time histories of ground motion (GM) on a 5-km grid of 625 stations in Southwest Iceland (SI). The ruptures were defined on a new synthetic time-independent 500-year catalog consisting of 223 hypothetical fin…

Pretzel monoids
Daniel Heath, Mark Kambites, N\'ora Szak\'acs
https://arxiv.org/abs/2405.00589 https://arxiv.org/pdf/2405.005…

Pretzel monoids
We introduce an interesting class of left adequate monoids which we call pretzel monoids. These, on the one hand, are monoids of birooted graphs with respect to a natural `glue-and-fold' operation, and on the other hand, are shown to be defined in the category of left adequate monoids by a natural class of presentations. They are also shown to be the free idempotent-pure expansions of right cancellative monoids, making them, in some sense, the left adequate analogues of Margolis-Meakin expansio…

This https://arxiv.org/abs/2301.11580 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

A Characterization of Complexity in Public Goods Games
We complete the characterization of the computational complexity of equilibrium in public goods games on graphs. In this model, each vertex represents an agent deciding whether to produce a public good, with utility defined by a "best-response pattern" determining the best response to any number of productive neighbors. We prove that the equilibrium problem is NP-complete for every finite non-monotone best-response pattern. This answers the open problem of [Gilboa and Nisan, 2022], and complete…

Action of the relative Weyl group on partial Springer sheaf
Tamanna Chatterjee, Laura Rider
https://arxiv.org/abs/2403.18959 https://…

Action of the relative Weyl group on partial Springer sheaf
In the context of the Springer correspondence, the Weyl group action on the Springer sheaf can be defined in two ways: via restriction or the Fourier transform. It is well-known that these two actions differ by the sign character. This was proven by Hotta for sheaves with characteristic 0 coefficients in 1981, and more recently extended to arbitrary coefficients by Achar, Henderson, Juteau, and Riche in 2014. In this short article, we study an extension of this problem to the partial Springer s…

This https://arxiv.org/abs/2401.10916 has been replaced.
initial toot: https://mastoxiv.page/@a…

Thermodynamics and Kinetics of Silicate Glasses submitted to Binary Ion Exchange: Equilibrium Conditions and Interdiffusion Kinetics
Ion exchange processes between an ion reservoir and a solid matrix are modeled under the assumption that near interface volumes reach equilibrium in a much faster time than the overall ion exchange process time while, in the bulk of the solid matrix, ions are transported by an interdiffusion kinetic process. Ion exchange equilibrium conditions are initially established according to classical thermodynamics. The result is defined in terms of the chemical potentials of exchanging ionic species. T…

This https://arxiv.org/abs/1808.00489 has been replaced.
link: https://scholar.google.com/scholar?q=a

Describing Quasi-Graphic Matroids
The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids and lifted-graphic matroids introduced earlier by Zaslavsky. For each biased graph $(G, \mathcal B)$ Zaslavsky defined a unique lift matroid $L(G, \mathcal B)$ and a unique frame matroid $F(G, \mathcal B)$, each on ground set $E(G)$. We show that in general there may be many quasi-graphic matroids on $E(G)$ and describe them all. We provide cryptomorphic desc…

This https://arxiv.org/abs/2209.10282 has been replaced.
link: https://scholar.google.com/scholar?q=a

The integration theory of curved absolute L-infinity algebras
In this article, we introduce the notion of a curved absolute $\mathcal{L}_\infty$-algebra, a structure that behaves like a curved $\mathcal{L}_\infty$-algebra where all infinite sums of operations are well-defined by definition. We develop their integration theory by introducing two new methods in integration theory: the complete Bar construction and intrinsic model category structures. They allow us to generalize all essential results of this theory quickly and from a conceptual point of view…

This https://arxiv.org/abs/2404.16693 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Mutual transformations of arbitrary ternary qubit trees by Clifford gates
It is shown that ternary qubit trees with the same number of nodes can be transformed by the naturally defined sequence of Clifford gates into each other or into standard representation as 1D chain corresponding to Jordan-Wigner transform.

This https://arxiv.org/abs/2312.07193 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

$(σ,δ)$-polycyclic codes in Ore extensions over rings
In this paper, we study the algebraic structure of $(σ,δ)$-polycyclic codes, defined as submodules in the quotient module $S/Sf$, where $S=R[x,σ,δ]$ is the Ore extension ring, $f\in S$, and $R$ is a finite but not necessarily commutative ring. We establish that the Euclidean duals of $(σ,δ)$-polycyclic codes are $(σ,δ)$-sequential codes. By using $(σ,δ)$-Pseudo Linear Transformation, we define the annihilator dual of $(σ,δ)$-polycyclic codes. Then, we demonstrate that the annihilato…

Generalized Pentagon Equations
Anton Alekseev, Florian Naef, Muze Ren
https://arxiv.org/abs/2402.19138 https://arxiv.org/pdf/2402.191…

Generalized Pentagon Equations
Drinfeld defined the Knizhinik--Zamolodchikov (KZ) associator $Φ_{\rm KZ}$ by considering the regularized holonomy of the KZ connection along the {\em droit chemin} $[0,1]$. The KZ associator is a group-like element of the free associative algebra with two generators, and it satisfies the pentagon equation. In this paper, we consider paths on $\mathbb{C}\backslash \{ z_1, \dots, z_n\}$ which start and end at tangential base points. These paths are not necessarily straight, and they may have …

Exploring the Capability of LLMs in Performing Low-Level Visual Analytic Tasks on SVG Data Visualizations
Zhongzheng Xu, Emily Wall
https://arxiv.org/abs/2404.19097 https://arxiv.org/pdf/2404.19097
arXiv:2404.19097v1 Announce Type: new
Abstract: Data visualizations help extract insights from datasets, but reaching these insights requires decomposing high level goals into low-level analytic tasks that can be complex due to varying data literacy and experience. Recent advancements in large language models (LLMs) have shown promise for lowering barriers for users to achieve tasks such as writing code. Scalable Vector Graphics (SVG), a text-based image format common in data visualizations, matches well with the text sequence processing of transformer-based LLMs. In this paper, we explore the capability of LLMs to perform low-level visual analytic tasks defined by Amar, Eagan, and Stasko directly on SVG-based visualizations. Using zero-shot prompts, we instruct the models to provide responses or modify the SVG code based on given visualizations. Our findings demonstrate that LLMs can effectively modify existing SVG visualizations for specific tasks like Cluster but perform poorly on tasks requiring a sequence of math operations. We also discovered that LLM performance varies based on factors such as the number of data points, the presence of value labels, and the chart type. Our findings contribute to gauging the general capabilities of LLMs and highlight the need for further exploration and development to fully harness their potential in supporting visual analytic tasks.

This https://arxiv.org/abs/2401.15972 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fibonacci vector and matrix p-norms
This paper delves into vector and matrix norms of Fibonacci numbers. Two classes of Fibonacci vectors and a parametric p-norm are defined. From this definition, several properties of Fibonacci vector and matrix p-norms are described by varying parameter p. A closed-form expression is given to obtain the value of p, setting the difference between the p-norm and the infinite norm below a given threshold. A new class of symmetric k-Fibonacci matrix is defined such that a simple reorganization simp…

This https://arxiv.org/abs/2209.10842 has been replaced.
link: https://scholar.google.com/scholar?q=a

The complex hyperbolic form as a Weil-Petersson form
For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation of the complex hyperbolic form, i.e. the Kähler form of the complex hyperbolic structure on the moduli space, as a kind of Weil-Petersson form.

This https://arxiv.org/abs/2209.10282 has been replaced.
link: https://scholar.google.com/scholar?q=a

The integration theory of curved absolute L-infinity algebras
In this article, we introduce the notion of a curved absolute $\mathcal{L}_\infty$-algebra, a structure that behaves like a curved $\mathcal{L}_\infty$-algebra where all infinite sums of operations are well-defined by definition. We develop their integration theory by introducing two new methods in integration theory: the complete Bar construction and intrinsic model category structures. They allow us to generalize all essential results of this theory quickly and from a conceptual point of view…

Total Completion Time Scheduling Under Scenarios
Thomas Bosman, Martijn van Ee, Ekin Ergen, Csanad Imreh, Alberto Marchetti-Spaccamela, Martin Skutella, Leen Stougie
https://arxiv.org/abs/2402.19259

Total Completion Time Scheduling Under Scenarios
Scheduling jobs with given processing times on identical parallel machines so as to minimize their total completion time is one of the most basic scheduling problems. We study interesting generalizations of this classical problem involving scenarios. In our model, a scenario is defined as a subset of a predefined and fully specified set of jobs. The aim is to find an assignment of the whole set of jobs to identical parallel machines such that the schedule, obtained for the given scenarios by si…

Construction of free arrangements using point-line operators
Piotr Pokora, Xavier Roulleau
https://arxiv.org/abs/2403.20024 https://a…

Construction of free arrangements using point-line operators
We construct new examples of free curve arrangements in the complex projective plane using point-line operators recently defined by the second author. In particular, we construct a new example of a conic-line arrangement with ordinary quasi-homogeneous singularities that has non-trivial monodromy.

Optimal regimes with limited resources
Aaron L. Sarvet, Julien D. Laurendeau, Mats J. Stensrud
https://arxiv.org/abs/2403.19842 https://

Optimal regimes with limited resources
Policy-makers are often faced with the task of distributing a limited supply of resources. To support decision-making in these settings, statisticians are confronted with two challenges: estimands are defined by allocation strategies that are functions of features of all individuals in a cluster; and relatedly the observed data are neither independent nor identically distributed when individuals compete for resources. Existing statistical approaches are inadequate because they ignore at least o…

This https://arxiv.org/abs/2312.12173 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Globally Convergent Policy Gradient Method for Linear Quadratic Gaussian (LQG) Control
We present a model-based globally convergent policy gradient method (PGM) for linear quadratic Gaussian (LQG) control. Firstly, we establish equivalence between optimizing dynamic output feedback controllers and designing a static feedback gain for a system represented by a finite-length input-output history (IOH). This IOH-based approach allows us to explore LQG controllers within a parameter space defined by IOH gains. Secondly, by considering a control law comprising the IOH gain and a suffi…

Proving Behavioural Apartness
Ruben Turkenburg, Harsh Beohar, Clemens Kupke, Jurriaan Rot
https://arxiv.org/abs/2404.16588 https://ar…

Proving Behavioural Apartness
Bisimilarity is a central notion for coalgebras. In recent work, Geuvers and Jacobs suggest to focus on apartness, which they define by dualising coalgebraic bisimulations. This yields the possibility of finite proofs of distinguishability for a wide variety of state-based systems. We propose behavioural apartness, defined by dualising behavioural equivalence rather than bisimulations. A motivating example is the subdistribution functor, where the proof system based on bisimilarity requires a…

Adaptive Energy Regularization for Autonomous Gait Transition and Energy-Efficient Quadruped Locomotion
Boyuan Liang, Lingfeng Sun, Xinghao Zhu, Bike Zhang, Ziyin Xiong, Chenran Li, Koushil Sreenath, Masayoshi Tomizuka
https://arxiv.org/abs/2403.20001

Adaptive Energy Regularization for Autonomous Gait Transition and Energy-Efficient Quadruped Locomotion
In reinforcement learning for legged robot locomotion, crafting effective reward strategies is crucial. Pre-defined gait patterns and complex reward systems are widely used to stabilize policy training. Drawing from the natural locomotion behaviors of humans and animals, which adapt their gaits to minimize energy consumption, we propose a simplified, energy-centric reward strategy to foster the development of energy-efficient locomotion across various speeds in quadruped robots. By implementing…

Orbifold Euler Characteristics of Compactified Jacobians
Sofia Wood
https://arxiv.org/abs/2402.19368 https://arxiv.org/pdf/2402.19368…

Orbifold Euler Characteristics of Compactified Jacobians
We calculate the orbifold Euler characteristics of all the degree d fine universal compactified Jacobians (defined by Pagani and Tommasi) over the moduli space of stable curves of genus g with n marked points. We show that this orbifold Euler characteristic agrees with the Euler characteristic of the moduli space of stable, genus 0 curves with 2g+n markings up to a combinatorial factor, and in particular, is independent of the degree d and the choice of degree d universal fine compactified Jaco…

This https://arxiv.org/abs/2311.08387 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hilbert evolution algebras, weighted digraphs, and nilpotency
Hilbert evolution algebras generalize evolution algebras through a framework of Hilbert spaces. In this work we focus on infinite-dimensional Hilbert evolution algebras and their representation through a suitably defined weighted digraph. By means of studying such a digraph we obtain new properties for these structures extending well-known results related to the nilpotency of finite dimensional evolution algebras. We show that differently from what happens for the finite dimensional evolution a…

On the codimension of permanental varieties
Ada Boralevi, Enrico Carlini, Mateusz Micha{\l}ek, Emanuele Ventura
https://arxiv.org/abs/2402.17839 https://…

On the codimension of permanental varieties
In this article, we study permanental varieties, i.e. varieties defined by the vanishing of permanents of fixed size of a generic matrix. Permanents and their varieties play an important, and sometimes poorly understood, role in combinatorics. However, there are essentially no geometric results about them in the literature, in very sharp contrast to the well-behaved and ubiquitous case of determinants and minors. Motivated by the study of the singular locus of the permanental hypersurface, we f…

This https://arxiv.org/abs/2105.04334 has been replaced.
link: https://scholar.google.com/scholar?q=a

Asymptotic Analysis of q-Recursive Sequences
For an integer $q\ge2$, a $q$-recursive sequence is defined by recurrence relations on subsequences of indices modulo some powers of~$q$. In this article, $q$-recursive sequences are studied and the asymptotic behavior of their summatory functions is analyzed. It is shown that every $q$-recursive sequence is $q$-regular in the sense of Allouche and Shallit and that a $q$-linear representation of the sequence can be computed easily by using the coefficients from the recurrence relations. Detaile…

Local Invariants on an ICIS
Raphael de Omena
https://arxiv.org/abs/2403.20226 https://arxiv.org/pdf/2403.20226

Local Invariants on an ICIS
This work investigates invariants, including the GSV-index, local Euler obstruction, and Brasselet number, within the context of isolated complete intersection singularities (ICIS). The aim is to establish connections between these invariants, allowing for the extraction of topological and geometric information through algebraic methods. The Bruce-Roberts number plays a central role in achieving this objective, since is defined by algebraic tools.

This https://arxiv.org/abs/2311.08387 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hilbert evolution algebras, weighted digraphs, and nilpotency
Hilbert evolution algebras generalize evolution algebras through a framework of Hilbert spaces. In this work we focus on infinite-dimensional Hilbert evolution algebras and their representation through a suitably defined weighted digraph. By means of studying such a digraph we obtain new properties for these structures extending well-known results related to the nilpotency of finite dimensional evolution algebras. We show that differently from what happens for the finite dimensional evolution a…

This https://arxiv.org/abs/2105.04334 has been replaced.
link: https://scholar.google.com/scholar?q=a

Asymptotic Analysis of q-Recursive Sequences
For an integer $q\ge2$, a $q$-recursive sequence is defined by recurrence relations on subsequences of indices modulo some powers of~$q$. In this article, $q$-recursive sequences are studied and the asymptotic behavior of their summatory functions is analyzed. It is shown that every $q$-recursive sequence is $q$-regular in the sense of Allouche and Shallit and that a $q$-linear representation of the sequence can be computed easily by using the coefficients from the recurrence relations. Detaile…

Leading terms of generalized Pl\"ucker formulas
Andr\'as P. Juh\'asz
https://arxiv.org/abs/2404.18859 https://arxiv.org/…

Leading terms of generalized Plücker formulas
Generalized Plücker numbers are defined to count certain types of tangent lines of generic degree $d$ complex projective hypersurfaces. They can be computed by identifying them as coefficients of GL(2)-equivariant cohomology classes of certain invariant subspaces, the so-called coincident root strata, of the vector space of homogeneous degree $d$ complex polynomials in two variables. In an earlier paper László M. Fehér and the author gave a new, recursive method for calculating these classe…

Symmetry defect of $n$-dimensional complete intersections in $\mathbb{C}^{2n-1}$
L. R. G. Dias, Z. Jelonek
https://arxiv.org/abs/2404.18927 https://…

Symmetry defect of $n$-dimensional complete intersections in $\mathbb{C}^{2n-1}$
Let $X, Y \subset \mathbb{C}^{2n-1}$ be $n$-dimensional strong complete intersections in a general position. In this note, we consider the set of midpoints of chords connecting a point $x \in X$ to a point $y \in Y$. This set is defined as the image of the map $Φ(x,y)=\frac{x+y}{2}.$ Under geometric conditions on $X$ and $Y$, we prove that the symmetry defect of $X$ and $Y$, which is the bifurcation set $B(X,Y)$ of the mapping $Φ$, is an algebraic variety, characterized by a topological invar…

This https://arxiv.org/abs/2312.06930 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Quillen-Lichtenbaum dimension of complex varieties
The Quillen-Lichtenbaum conjecture for smooth complex varieties states that algebraic and topological K-theory with finite coefficients become isomorphic in high degrees. We define the "Quillen-Lichtenbaum dimension" of a variety in terms of the point where this happens, show that it is surprisingly computable, and analyze many examples. It gives an obstruction to rationality, but one that turns out to be weaker than unramified cohomology and some related birational invariants defined by Collio…