Tootfinder

A universal tale of determinants and Gr\"obner bases
Aldo Conca
https://arxiv.org/abs/2403.07098 https://arxiv.org/pdf/2403.0709…

A universal tale of determinants and Gröbner bases
In 1965 Buchberger defined Gröbner bases and an algorithm to compute them. Despite a slow start, already in the eighties Gröbner bases had become the main device for symbolic computations involving polynomials as well as a theoretical tool for the investigation of ideals and varieties via the so-called Gröbner deformation techniques. Rings and algebraic varieties defined by means of determinants are among the most classical objects in commutative algebra, algebraic geometry and invariant the…

This https://arxiv.org/abs/2304.11515 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Patterson-Sullivan measures for transverse subgroups
We study Patterson-Sullivan measures for a class of discrete subgroups of higher rank semisimple Lie groups, called transverse groups, whose limit set is well-defined and transverse in a partial flag variety. This class of groups includes both Anosov and relatively Anosov groups, as well as all discrete subgroups of rank one Lie groups. We prove an analogue of the Hopf-Tsuji-Sullivan dichotomy and then use this dichotomy to prove a variant of Burger's Manhattan curve theorem. We also use the Pa…

This https://arxiv.org/abs/2403.06752 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The $K_{1,2}$-structure-connectivity of graphs
n this paper, we mainly investigate $K_{1,2}$-structure-connectivity for any connected graph. Let $G$ be a connected graph with $n$ vertices, we show that $κ(G; K_{1,2})$ is well-defined if $diam(G)\geq 4$, or $n\equiv 1\pmod 3$, or $G\notin \{C_{5},K_{n}\}$ when $n\equiv 2\pmod 3$, or there exist three vertices $u,v,w$ such that $N_{G}(u)\cap (N_{G}(v,w)\cup\{v,w\})=\emptyset$ when $n\equiv 0\pmod 3$. Furthermore, if $G$ has $K_{1,2}$-structure-cut, we prove $κ(G)/3\leqκ(G; K_{1,2})\leqκ(G…

A time-adaptive finite element phase-field model suitable for rate-independent fracture mechanics
Felix R\"orentrop, Samira Boddin, Dorothee Knees, J\"orn Mosler
https://arxiv.org/abs/2403.07461

A time-adaptive finite element phase-field model suitable for rate-independent fracture mechanics
The modeling of cracks is an important topic - both in engineering as well as in mathematics. Since crack propagation is characterized by a free boundary value problem (the geometry of the crack is not known beforehand, but part of the solution), approximations of the underlying sharp-interface problem based on phase-field models are often considered. Focusing on a rate-independent setting, these models are defined by a unidirectional gradient-flow of an energy functional. Since this energy fun…

This https://arxiv.org/abs/2309.03628 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csNI_…

OSMOSIS: Enabling Multi-Tenancy in Datacenter SmartNICs
Multi-tenancy is essential for unleashing SmartNIC's potential in datacenters. Our systematic analysis in this work shows that existing on-path SmartNICs have resource multiplexing limitations. For example, existing solutions lack multi-tenancy capabilities such as performance isolation and QoS provisioning for compute and IO resources. Compared to standard NIC data paths with a well-defined set of offloaded functions, unpredictable execution times of SmartNIC kernels make conventional approach…

On Uniqueness of Participation Factors
Tianwei Xia, Kai Sun
https://arxiv.org/abs/2403.07156 https://arxiv.org/pdf/2403.07156<…

On Uniqueness of Participation Factors
In modal analysis and control of a nonlinear dynamical system, participation factors of state variables with respect to a mode of interest serve as pivotal tools for stability studies. Linear participation factors are uniquely determined by the mode's shape and composition, which are defined by the right and left eigenvectors of the linearized model. For nonlinear participation factors as well as five other variants of participation factors, this paper finds the sufficient conditions for them t…

Sheaves of $(\infty, \infty)$-categories
Zach Goldthorpe
https://arxiv.org/abs/2403.06926 https://arxiv.org/pdf/2403.06926

Sheaves of $(\infty, \infty)$-categories
We provide a functorial presentation of the $(\infty, 1)$-category of sheaves of $(n, r)$-categories for all $-2 \leq n\leq\infty$ and $0 \leq r\leq n+2$ baed on complete Segal space objects. In this definition, the equivalences of sheaves of $(\infty, \infty)$-categories are defined inductively, so we also provide a localisation at the coinductive equivalences to define the $(\infty, 1)$-category of sheaves of $ω$-categories as well. We prove that the $(\infty, 1)$-category of sheaves of $(\i…

This https://arxiv.org/abs/2402.10903 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Continuum limit of the Green function in scaled affine $φ^4_4$ quantum Euclidean covariant relativistic field theory
We prove through path integral Monte Carlo computer experiments that the affine quantization of the $φ_4^4$ scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well defined continuum limit of the one- and two-point-function. Affine quantization leads to a completely satisfactory quantization of field theories using situations that involve scaled behavior leading to an unexpected, $\hbar^2/φ^2$ which arises only in the quantum aspects.

#PromXtra in #ColwynBay today so out on the bike early before the crowds turn up. Nice shadows from the jetty at Raynes Quarry
#WelshPhotography

On Naisargik Images of Varshamov-Tenengolts and Helberg Codes
Kalp Pandya, Devdeep Shetranjiwala, Naisargi Savaliya, Manish K. Gupta
https://arxiv.org/abs/2404.07670

On Naisargik Images of Varshamov-Tenengolts and Helberg Codes
The VT and Helberg codes, both in binary and non-binary forms, stand as elegant solutions for rectifying insertion and deletion errors. In this paper we consider the quaternary versions of these codes. It is well known that many optimal binary non-linear codes like Kerdock and Prepreta can be depicted as Gray images (isometry) of codes defined over $\mathbb{Z}_4$. Thus a natural question arises: Can we find similar maps between quaternary and binary spaces which gives interesting properties whe…

TeraPool-SDR: An 1.89TOPS 1024 RV-Cores 4MiB Shared-L1 Cluster for Next-Generation Open-Source Software-Defined Radios
Yichao Zhang, Marco Bertuletti, Samuel Riedel, Matheus Cavalcante, Alessandro Vanelli-Coralli, Luca Benini
https://arxiv.org/abs/2405.04988

TeraPool-SDR: An 1.89TOPS 1024 RV-Cores 4MiB Shared-L1 Cluster for Next-Generation Open-Source Software-Defined Radios
Radio Access Networks (RAN) workloads are rapidly scaling up in data processing intensity and throughput as the 5G (and beyond) standards grow in number of antennas and sub-carriers. Offering flexible Processing Elements (PEs), efficient memory access, and a productive parallel programming model, many-core clusters are a well-matched architecture for next-generation software-defined RANs, but staggering performance requirements demand a high number of PEs coupled with extreme Power, Performance…

Existence of Optimal Stationary Singular Controls and Mean Field Game Equilibria
Asaf Cohen, Chuhao Sun
https://arxiv.org/abs/2404.07945 https://

Existence of Optimal Stationary Singular Controls and Mean Field Game Equilibria
In this paper, we examine the stationary relaxed singular control problem within a multi-dimensional framework for a single agent, as well as its Mean Field Game (MFG) equivalent. We demonstrate that optimal relaxed controls exist for both maximization and minimization cases. These relaxed controls are defined by random measures across the state and control spaces, with the state process described as a solution to the associated martingale problem. By leveraging findings from [Kurtz-Stockbridge…

My, what a regular and well defined dip in my solar production today, on a day without clouds.
I wonder what could have been the cause?
#eclipse

This https://arxiv.org/abs/2312.04487 has been replaced.
link: https://scholar.google.com/scholar?q=a

On The Maximum Linear Arrangement Problem for Trees
Linear arrangements of graphs are a well-known type of graph labeling and are found in many important computational problems, such as the Minimum Linear Arrangement Problem ($\texttt{minLA}$). A linear arrangement is usually defined as a permutation of the $n$ vertices of a graph. An intuitive geometric setting is that of vertices lying on consecutive integer positions in the real line, starting at 1; edges are often drawn as semicircles above the real line. In this paper we study the Maximum L…

Refutability as Recursive as Provability
Paola Cattabriga
https://arxiv.org/abs/2404.04038 https://arxiv.org/pdf/2404.04038

Refutability as Recursive as Provability
Godel numbering is an arithmetization of sintax which defines provability by coding a primitive recursive predicate, Pf(x,v). A multiplicity of researches and results all around this well-known recursive predicate are today widespread in many areas of logic and AI. Not equally investigated is the refutability predicate defined by Godel numbering within the same primitive recursive status. Rf(x,v) can be defined as a recursive predicate meaning that x is the Godel number of a refutation in PA of…

This https://arxiv.org/abs/2401.17078 has been replaced.
initial toot: https://mastoxiv.page/@…

Quantum propagating front and the edge of the Wigner function
In the first part of the article, we study one-dimensional noninteracting fermions in the continuum and in the presence of the repulsive inverse power law potential, with an emphasis on the Wigner function in the semiclassical limit. In this limit, the Wigner function exhibits an edge called the Fermi surf that depends only on the classical one-particle Hamiltonian. Around the Fermi surf, under a well-defined semiclassical limit, the Wigner function can be expressed in terms of Airy functions w…

This https://arxiv.org/abs/2402.05812 has been replaced.
link: https://scholar.google.com/scholar?q=a

FAQ-Gen: An automated system to generate domain-specific FAQs to aid content comprehension
Frequently Asked Questions (FAQs) refer to the most common inquiries about specific content. They serve as content comprehension aids by simplifying topics and enhancing understanding through succinct presentation of information. In this paper, we address FAQ generation as a well-defined Natural Language Processing task through the development of an end-to-end system leveraging text-to-text transformation models. We present a literature review covering traditional question-answering systems, hi…

Entanglement entropy in the ground state of non-interacting massless Dirac fermions in dimension one
Fabrizio Ferro, Paul Pfeiffer, Wolfgang Spitzer
https://arxiv.org/abs/2404.07068

Entanglement entropy in the ground state of non-interacting massless Dirac fermions in dimension one
We present a novel proof of a formula of Casini and Huerta for the entanglement entropy of the ground state of non-interacting massless Dirac fermions in dimension one localized to (a union of) intervals and generalize it to the case of Rényi entropies. At first, we prove that these entropies are well-defined for non-intersecting intervals. This is accomplished by an inequality of Alexander V.~Sobolev. Then we compute this entropy using a trace formula for Wiener--Hopf operators by Harold Wido…

A Clique-Based Separator for Intersection Graphs of Geodesic Disks in $\mathbb{R}^2$
Boris Aronov, Mark de Berg, Leonidas Theocharous
https://arxiv.org/abs/2403.04905

A Clique-Based Separator for Intersection Graphs of Geodesic Disks in $\mathbb{R}^2$
Let $d$ be a (well-behaved) shortest-path metric defined on a path-connected subset of $\mathbb{R}^2$ and let $\mathcal{D}=\{D_1,\ldots,D_n\}$ be a set of geodesic disks with respect to the metric $d$. We prove that $\mathcal{G}^{\times}(\mathcal{D})$, the intersection graph of the disks in $\mathcal{D}$, has a clique-based separator consisting of $O(n^{3/4+\varepsilon})$ cliques. This significantly extends the class of objects whose intersection graphs have small clique-based separators. Our…

Gate-defined quantum point contacts in a germanium quantum well
Han Gao, Zhen-Zhen Kong, Po Zhang, Yi Luo, Haitian Su, Xiao-Fei Liu, Gui-Lei Wang, Ji-Yin Wang, H. Q. Xu
https://arxiv.org/abs/2405.03107

Gate-defined quantum point contacts in a germanium quantum well
We report an experimental study of quantum point contacts defined in a high-quality strained germanium quantum well with layered electric gates. At zero magnetic field, we observe quantized conductance plateaus in units of 2$e^2/h$. Bias-spectroscopy measurements reveal that the energy spacing between successive one-dimensional subbands ranges from 1.5 to 5\,meV as a consequence of the small effective mass of the holes and the narrow gate constrictions. At finite magnetic fields perpendicular t…

This https://arxiv.org/abs/2312.14911 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Zero-bin subtraction and the $q_{\mathrm{T}}$ spectrum beyond leading power
In this paper, we present an algorithm to construct the qT distribution at NLO accuracy to arbitrary power precision, including the assembly of suitable zero-bin subtrahends, in a mathematically well-defined way for a generic choice of rapidity-divergence regularisation prescription. In its derivation, we divide the phase space into two sectors, the interior of the integration domain as well as the integration boundary, which we include here for the first time. To demonstrate the applicability …

My, what a regular and well defined dip in my solar production today, on a day without clouds.
I wonder what could have been the cause?
#eclipse

Numerical approximation of SDEs driven by fractional Brownian motion for all $H\in(0,1)$ using WIS integration
Utku Erdogan, Gabriel J. Lord, Roy B. Schieven
https://arxiv.org/abs/2404.07013

Numerical approximation of SDEs driven by fractional Brownian motion for all $H\in(0,1)$ using WIS integration
We examine the numerical approximation of a quasilinear stochastic differential equation (SDE) with multiplicative fractional Brownian motion. The stochastic integral is interpreted in the Wick-Itô-Skorohod (WIS) sense that is well defined and centered for all $H\in(0,1)$. We give an introduction to the theory of WIS integration before we examine existence and uniqueness of a solution to the SDE. We then introduce our numerical method which is based on the theoretical results in \cite{Mishura2…

This https://arxiv.org/abs/2207.02880 has been replaced.
link: https://scholar.google.com/scholar?q=a

The coalescent in finite populations with arbitrary, fixed structure
The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To unify and further generalize these variants, we introduce an abstract formulation of the coalescent that applies to a broad class of neutral drift models. Our formalism allows …

This https://arxiv.org/abs/2309.15382 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The multiplier spectrum morphism is generically injective
In this paper, we consider the multiplier spectrum of periodic points, which is a natural morphism defined on the moduli space of rational maps on the projective line. A celebrated theorem of McMullen asserts that aside from the well-understood flexible Lattès family, the multiplier spectrum morphism is quasi-finite. In this paper, we strengthen McMullen's theorem by showing that the multiplier spectrum morphism is generically injective. This answers a question of McMullen and Poonen.

On products of K-moduli spaces
Thedoros S. Papazachariou
https://arxiv.org/abs/2403.04544 https://arxiv.org/pdf/2403.04544

On products of K-moduli spaces
We study the K-moduli space of products of Fano varieties in relation to the product of K-moduli spaces of the product components. We show that there exists a well-defined morphism from the product of K-moduli stacks of Fano varieties to the K-moduli stack of their product. We further show that this morphism is an isomorphism if the two varieties are non-isomorphic, and a torsor if they are. Our results rely on the theory of stacks, and we extend them to general Artin stacks admitting good modu…

Sedimentary rocks from Mediterranean drought in the Messinian age as a probe of the past cosmic ray flux
Lorenzo Caccianiga, Claudio Galelli, Lorenzo Apollonio, Federico Maria Mariani, Paolo Magnani, Alessandro Veutro
https://arxiv.org/abs/2405.04908

Sedimentary rocks from Mediterranean drought in the Messinian age as a probe of the past cosmic ray flux
We propose the use of natural minerals as detectors to study the past flux of cosmic rays. This novel application of the \textit{paleo-detector} technique requires a specific approach as it needs samples that have been exposed to secondary cosmic rays for a well defined period of time. We suggest here the use of the evaporites formed during the desiccation of the Mediterranean sea ${\sim}6$ Myr ago. These minerals have been created and exposed to the air or under a shallow water basin for ${\si…

This https://arxiv.org/abs/2308.03425 has been replaced.
link: https://scholar.google.com/scholar?q=a

PPU: Design and Implementation of a Pipelined Full Posit Processing Unit
By exploiting the modular RISC-V ISA this paper presents the customization of instruction set with posit\textsuperscript{\texttrademark} arithmetic instructions to provide improved numerical accuracy, well-defined behavior and increased range of representable numbers while keeping the flexibility and benefits of open-source ISA, like no licensing and royalty fee and community development. In this work we present the design, implementation and integration into the low-power Ibex RISC-V core of a…

This https://arxiv.org/abs/2303.14181 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Transformations of Currents in Sigma-Models with Target Space Supersymmetry
We develop a framework for systematic study of symmetry transformations of sigma-model currents in a special situation, when symmetries have a well-defined projection onto the target space. We then apply this formalism to pure spinor sigma-models, and describe the resulting geometric structures in the target space (which in our approach includes the pure spinor ghosts). We perform a detailed study of the transformation properties of currents, using the formalism of equivariant cohomology. We cl…

This https://arxiv.org/abs/2312.14908 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Adjoint Representation of a Higher Lie Groupoid
We extend the standard construction of the adjoint representation of a Lie groupoid to the case of an arbitrary higher Lie groupoid. As for a Lie groupoid, the adjoint representation of a higher Lie groupoid turns out to be a representation up to homotopy which is well defined up to isomorphism. Its existence and uniqueness are immediate consequences of a more general result in the theory of simplicial vector bundles: the representation up to homotopy obtained by splitting a higher vector bundl…

This https://arxiv.org/abs/2401.00079 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Computable Scott sentences and the weak Whitehead problem for finitely presented groups
We prove that if $A$ is a computable Hopfian finitely presented structure, then $A$ has a computable $d$-$Σ_2$ Scott sentence if and only if the weak Whitehead problem for $A$ is decidable. We use this to infer that every hyperbolic group as well as any polycyclic-by-finite group has a computable $d$-$Σ_2$ Scott sentence, thus covering two main classes of finitely presented groups. Our proof also implies that every weakly Hopfian finitely presented group is strongly defined by its $\exists^+$…

Characterizing Lipschitz images of injective metric spaces
Judyta B\k{a}k, Taras Banakh, Joanna Garbuli\'nska-W\k{e}grzyn, Magdalena Nowak, Micha{\l} Pop{\l}awski
https://arxiv.org/abs/2405.01860

Characterizing Lipschitz images of injective metric spaces
A metric space $X$ is {\em injective} if every non-expanding map $f:B\to X$ defined on a subspace $B$ of a metric space $A$ can be extended to a non-expanding map $\bar f:A\to X$. We prove that a metric space $X$ is a Lipschitz image of an injective metric space if and only if $X$ is Lipschitz connected in the sense that for every points $x,y\in X$, there exists a Lipschitz map $f:[0,1]\to X$ such that $f(0)=x$ and $f(1)=y$. In this case the metric space $X$ carries a well-defined intrinsic met…

This https://arxiv.org/abs/2402.05812 has been replaced.
link: https://scholar.google.com/scholar?q=a

FAQ-Gen: An automated system to generate domain-specific FAQs to aid content comprehension
Frequently Asked Questions (FAQs) refer to the most common inquiries about specific content. They serve as content comprehension aids by simplifying topics and enhancing understanding through succinct presentation of information. In this paper, we address FAQ generation as a well-defined Natural Language Processing task through the development of an end-to-end system leveraging text-to-text transformation models. We present a literature review covering traditional question-answering systems, hi…

This https://arxiv.org/abs/2404.08529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

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…

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…

Transportability of Principal Causal Effects
Justin M. Clark, Kollin W. Rott, James S. Hodges, Jared D. Huling
https://arxiv.org/abs/2405.04419 https://

Transportability of Principal Causal Effects
Recent research in causal inference has made important progress in addressing challenges to the external validity of trial findings. Such methods weight trial participant data to more closely resemble the distribution of effect-modifying covariates in a well-defined target population. In the presence of participant non-adherence to study medication, these methods effectively transport an intention-to-treat effect that averages over heterogeneous compliance behaviors. In this paper, we develop a…

This https://arxiv.org/abs/2405.04683 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multicomplex Ideals, Modules and Hilbert Spaces
In this article we study some algebraic aspects of multicomplex numbers $\mathbb M_n$. A canonical idempotent representation defined in terms of $n$ multicomplex conjugates is introduced. This representation facilitates computations in this algebra and makes it possible to introduce a generalized conjugacy, i.e. a composition of the $n$ multicomplex conjugates, as well as a multicomplex norm. The ideals of the ring of multicomplex numbers are then studied. Multicomplex free modules and their li…

what if the reason I keep thinking in terms of "let's solve this thing with an event bus like homeassistant" or "this can be FNaaS like AWS"
is kinda like bikeshedding
or like me wishing human issues were computer code
or at least... synchronous, well defined, simplified computer code
"imagine democracy is a spherical cow"

Occasionally well-intentioned people argue that Arabs mostly aren't antisemites because Arabs are a semitic people. While the conclusion is clearly true this is nevertheless a bad argument. Words aren't defined by their etymology, and the word "antisemitism" has never meant anything more than hatred of Jews. No one would sensibly claim that homophobia means fear of sameness or transphobia means fear of acrossness, but it's the same argument. Even the Wiki has this one right -- it's their main example of the etymological fallacy.
#Antisemitism #EtymologicalFallacy

This https://arxiv.org/abs/2401.06096 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Precise characterization of a silicon carbide waveguide fiber interface
Emitters in high refractive index materials like 4H-SiC suffer from reduced detection of photons because of losses caused by total internal reflection. Thus, integration into efficient nanophotonic structures which couple the emission of photons to a well defined waveguide mode can significantly enhance the photon detection efficiency. In addition, interfacing this waveguide to a classical fiber network is of similar importance to detect the photons and perform experiments. Here, we show a wave…

Tower multitype and global regularity of the $\bar\partial$-Neumann operator
Dmitri Zaitsev
https://arxiv.org/abs/2405.02836 https://…

Tower multitype and global regularity of the $\bar\partial$-Neumann operator
A new approach is given to property $(P_q)$ defined by Catlin for $q=1$ in a global and by Sibony in a local context, subsequently extended by Fu-Straube for $q>1$. This property is known to imply compactness and global regularity in the $\bar\partial$-Neumann problem by a result of Kohn-Nirenberg, as well as condition $R$ by a result of Bell-Ligocka. In particular, we provide a self-contained proof of property $(P_q)$ for pseudoconvex hypersurfaces of finite D'Angelo $q$-type, the case origina…

Reduction of Cosymplectic Groupoids
Daniel L\'opez Garcia, Nicolas Martinez Alba
https://arxiv.org/abs/2403.03178 https://arxiv.o…

Reduction of Cosymplectic Groupoids
There is a well-known fact in Poisson geometry that reduction commutes with integration (of the associated integrable Lie algebroid). This is also valid for other types of geometries given by 2-dimensional closed forms. In this manuscript we extend this type of result to the particular case of cosymplectic groupoids, obtaining in particular the reduction of a central extension defined by a 2-IM form and a 1-IM form.

The injectivity radius of the compact Stiefel manifold under the Euclidean metric
Ralf Zimmermann, Jakob Stoye
https://arxiv.org/abs/2405.02268 https://

The injectivity radius of the compact Stiefel manifold under the Euclidean metric
The injectivity radius of a manifold is an important quantity, both from a theoretical point of view and in terms of numerical applications. It is the largest possible radius within which all geodesics are unique and length-minimizing. In consequence, it is the largest possible radius within which calculations in Riemannian normal coordinates are well-defined. A matrix manifold that arises frequently in a wide range of practical applications is the compact Stiefel manifold of orthogonal $p$-fra…

This https://arxiv.org/abs/2207.02880 has been replaced.
link: https://scholar.google.com/scholar?q=a

The coalescent in finite populations with arbitrary, fixed structure
The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To unify and further generalize these variants, we introduce an abstract formulation of the coalescent that applies to a broad class of neutral drift models. Our formalism allows …

On activation in solid ionic electrolytes
Keian Noori, Ben A. Olsen, Aleksandr Rodin
https://arxiv.org/abs/2404.06707 https://arxiv.o…

On activation in solid ionic electrolytes
Ionic conductivity in solid electrolytes is commonly expected to exhibit Arrhenius dependence on temperature, determined by a well-defined activation energy. Consequently, a standard approach involves calculating this energy using quasi-static methods and using the Arrhenius form to extrapolate the numerical results from one temperature range to another. Despite the ubiquity of this Arrhenius-based modeling, disagreements frequently arise between theory and experiment, and even between differen…

This https://arxiv.org/abs/2207.02203 has been replaced.
link: https://scholar.google.com/scholar?q=a

Noncrystalline topological superconductors
Topological insulators, featuring bulk-boundary correspondence, have been realized on a large number of noncrystalline materials, among which amorphous network, quasicrystals and fractal lattices are the most prominent ones. By contrast, topological superconductors beyond the realm of quantum crystals are yet to be harnessed, as their nucleation takes place around a well-defined Fermi surface with a Fermi momentum, the existence of which rests on the underlying translational symmetry. Here we i…

Vacuum amplitudes and time-like causal unitary in the loop-tree duality
The LTD Collaboration, Selomit Ram\'irez-Uribe, Andr\'es E. Renter\'ia-Olivo, David F. Renter\'ia-Estrada, Jorge J. Mart\'inez de Lejarza, Prasanna K. Dhani, Leandro Cieri, Roger J. Hern\'andez-Pinto, German F. R. Sborlini, William J. Torres Bobadilla, Germ\'an Rodrigo

Vacuum amplitudes and time-like causal unitary in the loop-tree duality
We present the first proof-of-concept application to decay processes at higher perturbative orders of LTD causal unitary, a novel methodology that exploits the causal properties of vacuum amplitudes in the loop-tree duality (LTD) and is directly well-defined in the four physical dimensions of the space-time. The generation of loop- and tree-level contributions to the differential decay rates from a kernel multiloop vacuum amplitude is shown in detail, and explicit expressions are presented for …

Apart from AI-based image decoding from brain activity, can the human brain learn to (internally) decode images from activity in its auditory cortex? I.e., mental imagery from images encoded in sound?
Meant here is the highly specific encoding of images through visual-to-auditory sensory substitution, such that mental images are in principle well-defined (after training), contrary to a brief verbal prompt for generating a mental image.

Exploiting Positional Bias for Query-Agnostic Generative Content in Search
Andrew Parry, Sean MacAvaney, Debasis Ganguly
https://arxiv.org/abs/2405.00469 h…

Exploiting Positional Bias for Query-Agnostic Generative Content in Search
In recent years, neural ranking models (NRMs) have been shown to substantially outperform their lexical counterparts in text retrieval. In traditional search pipelines, a combination of features leads to well-defined behaviour. However, as neural approaches become increasingly prevalent as the final scoring component of engines or as standalone systems, their robustness to malicious text and, more generally, semantic perturbation needs to be better understood. We posit that the transformer atte…

Rigid Matroid Categories
Kevin Purbhoo
https://arxiv.org/abs/2403.03365 https://arxiv.org/pdf/2403.03365

Rigid Matroid Categories
We consider three forms of composition of matroids, each of which extends the category of bimatroids to a rigid monoidal category. Many well-known constructions are functorial or defined by morphisms in these categories. Motivating examples include: deletion and contraction, 2-sum, series and parallel connections, the Tutte polynomial, gammoids, positroids, matroids representable over an infinite field, M-convex sets, and matroids associated to stable polynomials.

This https://arxiv.org/abs/2401.00358 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Joint distribution in residue classes of families of polynomially-defined multiplicative functions
We study the distribution of families of multiplicative functions among the coprime residue classes to moduli varying uniformly in a wide range, obtaining analogues of the Siegel--Walfisz Theorem for large classes of multiplicative functions. We extend a criterion of Narkiewicz for families of multiplicative functions that can be controlled by values of polynomials at the first few prime powers, and establish results that are completely uniform in the modulus as well as optimal in most paramete…

This https://arxiv.org/abs/2212.11055 has been replaced.
link: https://scholar.google.com/scholar?q=a

Coalgebraic Satisfiability Checking for Arithmetic $μ$-Calculi
The coalgebraic $μ$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $μ$-calculus includes an exponential-time upper bound on satisfiability checking, which however relies on the availability of tableau rules for the next-step modalities that are sufficiently well-behaved in a formally defined sense; in particular, rule ma…

Strategy for Direct Detection of Chiral Phonons with Phase-Structured Free Electrons
Marc R. Bourgeois, Andrew W. Rossi, David J. Masiello
https://arxiv.org/abs/2405.01826

Strategy for Direct Detection of Chiral Phonons with Phase-Structured Free Electrons
Chiral phonons possessing valley pseudo angular momentum (PAM) underlie a diversity of quantum phenomena of fundamental and applied importance, but are challenging to probe directly. We show that deficiencies of typical momentum-resolved electron energy loss measurements that make it impossible to distinguish the PAM of chiral phonons can be overcome by introducing pinwheel free electron states with well-defined PAM. Transitions between such states generate 2D periodic arrays of in-plane field …

This https://arxiv.org/abs/2305.15698 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSE_…

Rethinking Diversity in Deep Neural Network Testing
Motivated by the success of traditional software testing, numerous diversity measures have been proposed for testing deep neural networks (DNNs). In this study, we propose a shift in perspective, advocating for the consideration of DNN testing as directed testing problems rather than diversity-based testing tasks. We note that the objective of testing DNNs is specific and well-defined: identifying inputs that lead to misclassifications. Consequently, a more precise testing approach is to priori…

A Novel Context driven Critical Integrative Levels (CIL) Approach: Advancing Human-Centric and Integrative Lighting Asset Management in Public Libraries with Practical Thresholds
Jing Lin, Nina Mylly, Per Olof Hedekvist, Jingchun Shen
https://arxiv.org/abs/2404.17554

A Novel Context driven Critical Integrative Levels (CIL) Approach: Advancing Human-Centric and Integrative Lighting Asset Management in Public Libraries with Practical Thresholds
This paper proposes the context driven Critical Integrative Levels (CIL), a novel approach to lighting asset management in public libraries that aligns with the transformative vision of human-centric and integrative lighting. This approach encompasses not only the visual aspects of lighting performance but also prioritizes the physiological and psychological well-being of library users. Incorporating a newly defined metric, Mean Time of Exposure (MTOE), the approach quantifies user-light intera…

The Phase Transition of Reissner-Nordstr\"om Black Holes
Bobin Li
https://arxiv.org/abs/2405.04543 https://arxiv.org/pdf/2405.04…

The Phase Transition of Reissner-Nordström Black Holes
Under the framework of thermodynamics, the phase transition of the black hole is a general issue in general relativity. In this work, the phase transition of charged black holes is discussed carefully. The metric tensor of thermodynamics is redefined in the charged black hole, based on the Ruppeiner geometry. With the well-defined metric tensor of thermodynamics, the scalar curvature of the charged black hole is obtained. It is indicated that the scalar curvature is diverged and infinite when t…

Subdifferentially polynomially bounded functions and Gaussian smoothing-based zeroth-order optimization
Ming Lei, Ting Kei Pong, Shuqin Sun, Man-Chung Yue
https://arxiv.org/abs/2405.04150

Subdifferentially polynomially bounded functions and Gaussian smoothing-based zeroth-order optimization
We introduce the class of subdifferentially polynomially bounded (SPB) functions, which is a rich class of locally Lipschitz functions that encompasses all Lipschitz functions, all gradient- or Hessian-Lipschitz functions, and even some non-smooth locally Lipschitz functions. We show that SPB functions are compatible with Gaussian smoothing (GS), in the sense that the GS of any SPB function is well-defined and satisfies a descent lemma akin to gradient-Lipschitz functions, with the Lipschitz co…

This https://arxiv.org/abs/2309.12968 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

PassViz: A Visualisation System for Analysing Leaked Passwords
Passwords remain the most widely used form of user authentication, despite advancements in other methods. However, their limitations, such as susceptibility to attacks, especially weak passwords defined by human users, are well-documented. The existence of weak human-defined passwords has led to repeated password leaks from websites, many of which are of large scale. While such password leaks are unfortunate security incidents, they provide security researchers and practitioners with good oppor…

Me: I have a well-defined, specific issue that I'd like to see resolved. I've created a ticket explaining it.
Them (days later): Let's have a meeting so we can discuss it.
Me: 🙄 ... Here's even more detail, maybe we don't need to meet.
Them: Here's the schedule for the meeting.
Me (in meeting): Hi, what do you need to know?
Them (in meeting): What problem are you having?
Me: 😡 Here's everything I told you in the ticket.
Them: Oh,…

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/2306.07080 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stationary completeness: the $N$-body short-range case
For a general class of $N$-body Schrödinger operators with short-range pair-potentials the wave and scattering matrices as well as the restricted wave operators are all defined at any non-threshold energy. This holds without imposing any a priori decay condition on channel eigenstates and even for models including long-range potentials of Dereziński-Enss type. In this paper we improve for short-range models on the known weak continuity properties in that we show that all non-threshold energie…

Key varieties for prime $\mathbb{Q}$-Fano threefolds defined by Jordan algebras of cubic forms. Part I
Hiromichi Takagi
https://arxiv.org/abs/2403.14991 ht…

Key varieties for prime $\mathbb{Q}$-Fano threefolds defined by Jordan algebras of cubic forms. Part I
The first aim of this paper is to construct a $13$-dimensional affine variety $\mathscr{H}_{\mathbb{A}}^{13}$ related with $\mathbb{P}^{2}\times\mathbb{P}^{2}$-fibration. It is well-known that the affine cone of the Segre embedded $\mathbb{P}^{2}\times\mathbb{P}^{2}$ is defined as the null loci of the so called $\sharp$-mapping of a 9-dimensional nondegenerate quadratic Jordan algebra $J$ of a cubic form. Inspired with this fact, we construct $\mathscr{H}_{\mathbb{A}}^{13}$ in the same way coor…

Rigid Matroid Categories
Kevin Purbhoo
https://arxiv.org/abs/2403.03365 https://arxiv.org/pdf/2403.03365

Rigid Matroid Categories
We consider three forms of composition of matroids, each of which extends the category of bimatroids to a rigid monoidal category. Many well-known constructions are functorial or defined by morphisms in these categories. Motivating examples include: deletion and contraction, 2-sum, series and parallel connections, the Tutte polynomial, gammoids, positroids, matroids representable over an infinite field, M-convex sets, and matroids associated to stable polynomials.

Inequalities and bounds for expected order statistics from transform-ordered families
Tommaso Lando Idir Arab, Paulo Eduardo Oliveira
https://arxiv.org/abs/2403.03802

Inequalities and bounds for expected order statistics from transform-ordered families
We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a transform order. Notably, this method exhibits broad applicability, particularly since several well-known nonparametric distribution families can be defined using relevant transform orders, including the convex and the star transform orders. In the context of conve…

Multicomplex Ideals, Modules and Hilbert Spaces
Derek Courchesne, S\'ebastien Tremblay
https://arxiv.org/abs/2405.04683 https://a…

Multicomplex Ideals, Modules and Hilbert Spaces
In this article we study some algebraic aspects of multicomplex numbers $\mathbb M_n$. A canonical idempotent representation defined in terms of $n$ multicomplex conjugates is introduced. This representation facilitates computations in this algebra and makes it possible to introduce a generalized conjugacy, i.e. a composition of the $n$ multicomplex conjugates, as well as a multicomplex norm. The ideals of the ring of multicomplex numbers are then studied. Multicomplex free modules and their li…

This https://arxiv.org/abs/2302.11863 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

JT Gravity on a Finite Lorentzian Strip: Time dependent Quantum Gravity Amplitudes
We formulate JT quantum gravity on a finite Lorentzian strip. Due to the spatial boundaries of the strip, it is possible to define left and right proper times. With respect to these times we compute non-perturbatively the quantum gravity (QG) time dependent transition amplitude. Lagrangian and Hamiltonian formulations are presented. Special attention is paid to the four corner terms (Hayward terms) in the action that are needed in order to have a well defined variational problem. From a detaile…

High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms
Jiangfu Wang, Huazhong Tang, Kailiang Wu
https://arxiv.org/abs/2402.15446

High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms
This paper proposes novel high-order accurate discontinuous Galerkin (DG) schemes for the one- and two-dimensional ten-moment Gaussian closure equations with source terms defined by a known potential function. Our DG schemes exhibit the desirable capability of being well-balanced (WB) for a known hydrostatic equilibrium state while simultaneously preserving positive density and positive-definite anisotropic pressure tensor. The well-balancedness is built on carefully modifying the solution stat…

A Note On Lookahead In Real Life And Computing
Burle Sharma, Rakesh Mohanty, Sucheta Panda
https://arxiv.org/abs/2403.17942 https://a…

A Note On Lookahead In Real Life And Computing
Past, Present and Future are considered to be three temporal and logical concepts which are well defined by human beings for their existence and growth. We, as human beings, have the privilege of using our intelligence to mentally execute an activity before physical occurrence of the same in the real world. Knowledge of the past, aplomb of present and visualisation for the future correspond to three concepts such as look-back, look-at and look-ahead respectively in real life as well as in diver…

This https://arxiv.org/abs/2308.01728 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

A new 2D formulation of modified General Relativity
It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a new, intrinsically two-dimensional, approach to this problem based on the Einstein action. This yields a well defined variational approach which results in new field equations that break diffeomorphism invariance. Our proposed approach does not require the int…

Getting Saturated with Induction
M\'arton Hajdu, Petra Hozzov\'a, Laura Kov\'acs, Giles Reger, Andrei Voronkov
https://arxiv.org/abs/2402.18954

Getting Saturated with Induction
Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search framework of first-order theorem proving. We describe our induction inference rules proving properties with inductively defined datatypes and integers. We also present additional reasoning heuristics for strengthening inductive reasoning, as well as for using induc…

This https://arxiv.org/abs/2306.02280 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Degree-$M$ Bethe and Sinkhorn Permanent Based Bounds on the Permanent of a Non-negative Matrix
The permanent of a non-negative square matrix can be well approximated by finding the minimum of the Bethe free energy functions associated with some suitably defined factor graph; the resulting approximation to the permanent is called the Bethe permanent. Vontobel gave a combinatorial characterization of the Bethe permanent via degree-$M$ Bethe permanents, which is based on degree-$M$ covers of the underlying factor graph. In this paper, we prove a degree-$M$-Bethe-permanent-based lower bound …

This https://arxiv.org/abs/2401.00358 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Joint distribution in residue classes of families of polynomially-defined multiplicative functions
We study the distribution of families of multiplicative functions among the coprime residue classes to moduli varying uniformly in a wide range, obtaining analogues of the Siegel--Walfisz Theorem for large classes of multiplicative functions. We extend a criterion of Narkiewicz for families of multiplicative functions that can be controlled by values of polynomials at the first few prime powers, and establish results that are completely uniform in the modulus as well as optimal in most paramete…

Strategy for Direct Detection of Chiral Phonons with Phase-Structured Free Electrons
Marc R. Bourgeois, Andrew W. Rossi, David J. Masiello
https://arxiv.org/abs/2405.01826

Strategy for Direct Detection of Chiral Phonons with Phase-Structured Free Electrons
Chiral phonons possessing valley pseudo angular momentum (PAM) underlie a diversity of quantum phenomena of fundamental and applied importance, but are challenging to probe directly. We show that deficiencies of typical momentum-resolved electron energy loss measurements that make it impossible to distinguish the PAM of chiral phonons can be overcome by introducing pinwheel free electron states with well-defined PAM. Transitions between such states generate 2D periodic arrays of in-plane field …

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/2401.00079 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Computable Scott sentences and the weak Whitehead problem for finitely presented groups
We prove that if $A$ is a computable Hopfian finitely presented structure, then $A$ has a computable $d$-$Σ_2$ Scott sentence if and only if the weak Whitehead problem for $A$ is decidable. We use this to infer that every hyperbolic group as well as any polycyclic-by-finite group has a computable $d$-$Σ_2$ Scott sentence, thus covering two main classes of finitely presented groups. Our proof also implies that every weakly Hopfian finitely presented group is strongly defined by its $\exists^+$…

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…

SetCSE: Set Operations using Contrastive Learning of Sentence Embeddings
Kang Liu
https://arxiv.org/abs/2404.17606 https://arxiv.org/…

SetCSE: Set Operations using Contrastive Learning of Sentence Embeddings
Taking inspiration from Set Theory, we introduce SetCSE, an innovative information retrieval framework. SetCSE employs sets to represent complex semantics and incorporates well-defined operations for structured information querying under the provided context. Within this framework, we introduce an inter-set contrastive learning objective to enhance comprehension of sentence embedding models concerning the given semantics. Furthermore, we present a suite of operations, including SetCSE intersect…

Classifying bulk-edge anomalies in the Dirac Hamiltonian
Hansueli Jud, Cl\'ement Tauber
https://arxiv.org/abs/2403.04465 https://…

Classifying bulk-edge anomalies in the Dirac Hamiltonian
We study the Dirac Hamiltonian in dimension two with a mass term and a large momentum regularization, and show that bulk-edge correspondence fails. Despite a well defined bulk topological index --the Chern number--, the number of edge modes depends on the boundary condition. The origin of this anomaly is rooted in the unbounded nature of the spectrum. It is detected with Levinson's theorem from scattering theory and quantified via an anomalous winding number at infinite energy, dubbed ghost cha…

This https://arxiv.org/abs/2306.02280 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Degree-$M$ Bethe and Sinkhorn Permanent Based Bounds on the Permanent of a Non-negative Matrix
The permanent of a non-negative square matrix can be well approximated by finding the minimum of the Bethe free energy functions associated with some suitably defined factor graph; the resulting approximation to the permanent is called the Bethe permanent. Vontobel gave a combinatorial characterization of the Bethe permanent via degree-$M$ Bethe permanents, which is based on degree-$M$ covers of the underlying factor graph. In this paper, we prove a degree-$M$-Bethe-permanent-based lower bound …

This https://arxiv.org/abs/2403.05980 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

A Path Integral for Chord Diagrams and Chaotic-Integrable Transitions in Double Scaled SYK
We study transitions from chaotic to integrable Hamiltonians in the double scaled SYK and $p$-spin systems. The dynamics of our models is described by chord diagrams with two species. We begin by developing a path integral formalism of coarse graining chord diagrams with a single species of chords, which has the same equations of motion as the bi-local ($GΣ$) Liouville action, yet appears otherwise to be different and in particular well defined. We then develop a similar formalism for two type…

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/2308.10506 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A relaxation method for binary optimizations on constrained Stiefel manifold
This paper focuses on a class of binary orthogonal optimization problems frequently arising in semantic hashing. Consider that this class of problems may have an empty feasible set, rendering them not well-defined. We introduce an equivalent model involving a restricted Stiefel manifold and a matrix box set, and then investigate its penalty problems induced by the $\ell_1$-distance from the box set and its Moreau envelope. The two penalty problems are always well-defined. Moreover, they serve a…

Classifying bulk-edge anomalies in the Dirac Hamiltonian
Hansueli Jud, Cl\'ement Tauber
https://arxiv.org/abs/2403.04465 https://…

Classifying bulk-edge anomalies in the Dirac Hamiltonian
We study the Dirac Hamiltonian in dimension two with a mass term and a large momentum regularization, and show that bulk-edge correspondence fails. Despite a well defined bulk topological index --the Chern number--, the number of edge modes depends on the boundary condition. The origin of this anomaly is rooted in the unbounded nature of the spectrum. It is detected with Levinson's theorem from scattering theory and quantified via an anomalous winding number at infinite energy, dubbed ghost cha…

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…

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/2403.06926 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sheaves of $(\infty, \infty)$-categories
We provide a functorial presentation of the $(\infty, 1)$-category of sheaves of $(n, r)$-categories for all $-2 \leq n\leq\infty$ and $0 \leq r\leq n+2$ baed on complete Segal space objects. In this definition, the equivalences of sheaves of $(\infty, \infty)$-categories are defined inductively, so we also provide a localisation at the coinductive equivalences to define the $(\infty, 1)$-category of sheaves of $ω$-categories as well. We prove that the $(\infty, 1)$-category of sheaves of $(\i…

A positive metric over DGKT vacua
Eran Palti, Nicol\`o Petri
https://arxiv.org/abs/2405.01084 https://arxiv.org/pdf/2405.01084…

A positive metric over DGKT vacua
We study the notion of a metric over the space of AdS solution in string theory, leading to an associated distance between them. Such a distance is the idea underlying the AdS distance conjecture. We utilise the previously developed prescription for extracting such a metric: taking an off-shell quadratic variation of the string theory effective action and then evaluating it over the space of on-shell solutions. It was shown that this prescription leads to a well-defined positive metric over M-t…

On the algebraizability of formal deformations in $K$-cohomology
Eoin Mackall
https://arxiv.org/abs/2403.19008 https://arxiv.org/pdf/…

On the algebraizability of formal deformations in $K$-cohomology
We show that algebraizability of the functors $R^1π_*\mathcal{K}^M_{2,X}$ and $R^2π_*\mathcal{K}^M_{2,X}$ is a stable birational invariant for smooth and proper varieties $π:X\rightarrow k$ defined over an algebraic extension $k$ of $\mathbb{Q}$. The same is true for the étale sheafifications of these functors as well. To get these results we introduce a notion of relative $K$-homology for schemes of finite type over a finite dimensional, Noetherian, excellent base scheme over a field. We…

This https://arxiv.org/abs/2402.15778 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Graphs with a given conditional diameter that maximize the Wiener index
The Wiener index $W(G)$ of a graph $G$ is one of the most well-known topological indices, which is defined as the sum of distances between all pairs of vertices of $G$. The diameter $D(G)$ of $G$ is the maximum distance between all pairs of vertices of $G$; the conditional diameter $D(G;s)$ is the maximum distance between all pairs of vertex subsets with cardinality $s$ of $G$. When $s=1$, the conditional diameter $D(G;s)$ is just the diameter $D(G)$. The authors in \cite{QS} characterized the …

This https://arxiv.org/abs/2403.06926 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sheaves of $(\infty, \infty)$-categories
We provide a functorial presentation of the $(\infty, 1)$-category of sheaves of $(n, r)$-categories for all $-2 \leq n\leq\infty$ and $0 \leq r\leq n+2$ baed on complete Segal space objects. In this definition, the equivalences of sheaves of $(\infty, \infty)$-categories are defined inductively, so we also provide a localisation at the coinductive equivalences to define the $(\infty, 1)$-category of sheaves of $ω$-categories as well. We prove that the $(\infty, 1)$-category of sheaves of $(\i…

This https://arxiv.org/abs/2306.07323 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Crossed product algebras and generalized entropy for subregions
An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a von Neumann factor of type III$_1$, in which entropy cannot be well-defined because such algebras do not admit a trace or density states. However, associated to the algebra is a modular group of automorphisms characterizing the local dynamics of degrees of freedom in the region, and the crossed product of the algebra with its modular group yields a type II$_\infty$ factor, in which traces and he…

This https://arxiv.org/abs/2402.15778 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Graphs with a given conditional diameter that maximize the Wiener index
The Wiener index $W(G)$ of a graph $G$ is one of the most well-known topological indices, which is defined as the sum of distances between all pairs of vertices of $G$. The diameter $D(G)$ of $G$ is the maximum distance between all pairs of vertices of $G$; the conditional diameter $D(G;s)$ is the maximum distance between all pairs of vertex subsets with cardinality $s$ of $G$. When $s=1$, the conditional diameter $D(G;s)$ is just the diameter $D(G)$. The authors in \cite{QS} characterized the …

This https://arxiv.org/abs/2204.02829 has been replaced.
link: https://scholar.google.com/scholar?q=a

On integral local Shimura varieties
We give a construction of "integral local Shimura varieties" which are formal schemes that generalize the well-known integral models of the Drinfeld $p$-adic upper half spaces. The construction applies to all classical groups, at least for odd $p$. These formal schemes also generalize the formal schemes defined by Rapoport-Zink via moduli of $p$-divisible groups, and are characterized purely in group-theoretic terms. More precisely, for a local $p$-adic Shimura datum $(G, b, μ)$ and a quasi-pa…

Point potentials on Euclidean space, hyperbolic space and sphere in any dimension
Jan Derezi\'nski, Christian Ga{\ss}, B{\l}a\.zej Ruba
https://arxiv.org/abs/2403.17583

Point potentials on Euclidean space, hyperbolic space and sphere in any dimension
In dimensions d= 1, 2, 3 the Laplacian can be perturbed by a point potential. In higher dimensions the Laplacian with a point potential cannot be defined as a self-adjoint operator. However, for any dimension there exists a natural family of functions that can be interpreted as Green's functions of the Laplacian with a spherically symmetric point potential. In dimensions 1, 2, 3 they are the integral kernels of the resolvent of well-defined self-adjoint operators. In higher dimensions they are …

This https://arxiv.org/abs/2311.10690 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

On the degrees of freedom count on singular phase space submanifolds
I discuss singular loci in the phase spaces of theories which lack globally well-defined numbers of dynamical modes. This is a topic which appears quite often in the recent literature on modified gravity. In particular, there were discussions about $R^2$ gravity around Minkowski space. It is a relatively simple case, and still there were some confusions. It clearly shows that one should be very accurate when trying to understand a potentially problematic theory through perturbations around a si…

Orbifold theta functions and mid-age invariants
Fenglong You
https://arxiv.org/abs/2403.17077 https://arxiv.org/pdf/2403.17077…

Orbifold theta functions and mid-age invariants
We use the orbifold approach to study theta functions in intrinsic mirror symmetry. We introduce a new type of orbifold invariants for snc pairs, called mid-age invariants, and use these invariants to define orbifold invariants associated with the broken line type. Then, we define the orbifold theta functions as generating functions of orbifold invariants with mid-ages. We show that these orbifold theta functions are well-defined and satisfy the multiplication rule.

This https://arxiv.org/abs/2311.10690 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

On the degrees of freedom count on singular phase space submanifolds
I discuss singular loci in the phase spaces of theories which lack globally well-defined numbers of dynamical modes. This is a topic which appears quite often in the recent literature on modified gravity. In particular, there were discussions about $R^2$ gravity around Minkowski space. It is a relatively simple case, and still there were some confusions. It clearly shows that one should be very accurate when trying to understand a potentially problematic theory through perturbations around a si…

Orbifold theta functions and mid-age invariants
Fenglong You
https://arxiv.org/abs/2403.17077 https://arxiv.org/pdf/2403.17077…

Orbifold theta functions and mid-age invariants
We use the orbifold approach to study theta functions in intrinsic mirror symmetry. We introduce a new type of orbifold invariants for snc pairs, called mid-age invariants, and use these invariants to define orbifold invariants associated with the broken line type. Then, we define the orbifold theta functions as generating functions of orbifold invariants with mid-ages. We show that these orbifold theta functions are well-defined and satisfy the multiplication rule.

Graphs with a given conditional diameter that maximize the Wiener index
Junfeng An, Yingzhi Tian
https://arxiv.org/abs/2402.15778 https://

Graphs with a given conditional diameter that maximize the Wiener index
The Wiener index $W(G)$ of a graph $G$ is one of the most well-known topological indices, which is defined as the sum of distances between all pairs of vertices of $G$. The diameter $D(G)$ of $G$ is the maximum distance between all pairs of vertices of $G$; the conditional diameter $D(G;s)$ is the maximum distance between all pairs of vertex subsets with cardinality $s$ of $G$. When $s=1$, the conditional diameter $D(G;s)$ is just the diameter $D(G)$. The authors in \cite{QS} characterized the …

Quantum fields on projective geometries
Daniel Spitz
https://arxiv.org/abs/2403.17996 https://arxiv.org/pdf/2403.17996

Quantum fields on projective geometries
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On Lie algebra level the related conjugacy limits act isomorphically to concatenations of contractions. We axiomatically introduce projective quantum fields on homogeneous space-time geometries, based on correspondingly generalized unitary transformation behavio…