Tootfinder

On Capped Higgs Positivity Cone
Dong-Yu Hong, Zhuo-Hui Wang, Shuang-Yong Zhou
https://arxiv.org/abs/2404.04479 https://arxiv.org/pdf/…

On Capped Higgs Positivity Cone
The Wilson coefficients of the Standard Model Effective Field Theory are subject to a series of positivity bounds. It has been shown that, while the positivity part of the UV partial wave unitarity leads to the Wilson coefficients living in a convex cone, further including the non-positivity part caps the cone from above. For the Higgs scattering, a capped positivity cone have been obtained using a simplified, linear unitarity conditions and without utilizing the full internal symmetries of the…

This https://arxiv.org/abs/2203.01896 has been replaced.
link: https://scholar.google.com/scholar?q=a

Triangulations of Flow Polytopes, Ample Framings, and Gentle Algebras
The cone of nonnegative flows for a directed acyclic graph (DAG) is known to admit regular unimodular triangulations induced by framings of the DAG. These triangulations restrict to triangulations of the flow polytope for strength one flows, which are called DKK triangulations. For a special class of framings called ample framings, these triangulations of the flow cone project to a complete fan. We characterize the DAGs that admit ample framings, and we enumerate the number of ample framings fo…

Mapping Cone and Morse Theory
David Clausen, Xiang Tang, Li-Sheng Tseng
https://arxiv.org/abs/2405.02272 https://arxiv.org/pdf/2405.0…

Mapping Cone and Morse Theory
On a smooth manifold, we associate to any closed differential form a mapping cone algebra. The cohomology of this mapping cone algebra can vary with the de Rham cohomology class of the closed form. We present a novel Morse theoretical description for the mapping cone cohomology. Specifically, we introduce a Morse complex for the mapping cone algebra which is generated by pairs of critical points with the differential defined by gradient flows and an integration of the closed form over spaces of…

This https://arxiv.org/abs/2310.13464 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Completely mixed linear games and irreducibility concepts for Z-transformations over self-dual cones
In the setting of a self-dual cone in a finite-dimensional inner product space, we consider (zero-sum) linear games. In our previous work, we showed that a Z-transformation with positive value is completely mixed. The present paper considers the case when the value is zero. Motivated by the matrix game result that a Z-matrix with value zero is completely mixed if and only if it is irreducible, we formulate our general results based on the concepts of cone-irreducibility and space-irreducibility…

This https://arxiv.org/abs/2312.04074 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Inner bounding the quantum entropy cone with subadditivity and subsystem coarse grainings
We show via explicit construction that all the extreme rays of both the three-party quantum entropy cone and the four-party stabilizer entropy cone can be obtained from subsystem coarse grainings of specific higher-party quantum states, namely extreme states characterized by saturating a (non-trivial) maximal set of instances of subadditivity. This suggests that the study of the ``subadditivity cone'', and the set of its extreme rays realizable in quantum mechanics, provides a powerful tool for…

I made a sketch of a traffic cone and also wrote up a blog post about the inspiration...
➡️ #art…

Traffic Cone Sketch
Proceed with caution...

This https://arxiv.org/abs/2211.15020 has been replaced.
link: https://scholar.google.com/scholar?q=a

Quasi-symmetries between metric spaces and rough quasi-isometries between their infinite hyperbolic cones
In this paper, we first prove that any power quasi-symmetry of two metric spaces induces a rough quasi-isometry between their infinite hyperbolic cones. Second, we prove that for a complete metric space $Z$, there exists a point $ω$ in the Gromov boundary of its infinite hyperbolic cone such that $Z$ can be seen as the Gromov boundary relative to $ω$ of its infinite hyperbolic cone. Third, we prove that for a visual Gromov hyperbolic metric space $X$ and a Gromov boundary point $ω$, $X$ is r…

On pointwise convergence of cone multipliers
Peng Chen, Danqing He, Xiaochun Li, Lixin Yan
https://arxiv.org/abs/2405.02607 https://a…

On pointwise convergence of cone multipliers
For $p\ge 2$, and $λ>\max\{n|\tfrac 1p-\tfrac 12|-\tfrac12, 0\}$, we prove the pointwise convergence of cone multipliers, i.e. $$ \lim_{t\to\infty}T_t^λ(f)\to f \text{ a.e.},$$ where $f\in L^p(\mathbb R^n)$ satisfies $supp\ \widehat f\subset\{ξ\in\mathbb R^n:\ 1<|ξ_n|<2\}$. Our main tools are weighted estimates for maximal cone operators, which are consequences of trace inequalities for cones.

This https://arxiv.org/abs/2210.02779 has been replaced.
link: https://scholar.google.com/scholar?q=a

Nef cones of fiber products and an application to the Cone Conjecture
We prove a decomposition theorem for the nef cone of smooth fiber products over curves, subject to the necessary condition that their Néron--Severi space decomposes. We apply it to describe the nef cone of so-called Schoen varieties, which are the higher dimensional analogues of the Calabi--Yau threefolds constructed by Schoen. Schoen varieties give rise to Calabi--Yau pairs, and in each dimension at least three, there exist Schoen varieties with non-polyhedral nef cone. We prove the Kawamata-…

Dynkin abelianisations of flag varieties
Shreepranav Varma Enugandla, Xin Fang, Ghislain Fourier, Christian Steinert
https://arxiv.org/abs/2404.05277 https…

Dynkin abelianisations of flag varieties
Cerulli Irelli and Lanini have shown that PBW degenerations of flag varieties in type A and C are actually Schubert varieties of higher rank. We introduce Dynkin cones to parameterise specific abelianisations of classical Lie algebras. Within this framework, we generalise their result to all degenerations of flag varieties defined by degree vectors originating from a Dynkin cone. This framework allows us to determine the extent to which a flag variety can be degenerate while still naturally bei…

This https://arxiv.org/abs/2302.02862 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Parabolic quasi-contact cone structures with an infinitesimal symmetry
We interpret the property of having an infinitesimal symmetry as a variational property in certain geometric structures. This is achieved by establishing a one-to-one correspondence between a class of cone structures with an infinitesimal symmetry and geometric structures arising from certain systems of ODEs that are variational. Such cone structures include pseudo-Riemannian conformal structures and distributions of growth vector (2,3,5) and (3,6). The correspondence is obtained via symmetry r…

@…
https://mastodon.social/@PhilStooke/112208959593782148#.

Phil Stooke (@PhilStooke@mastodon.social)
Attached: 1 image Firefly Aerospace's Blue Ghost lander will go to a site in Mare Crisium north of the Luna 24 site. The landing site was originally one of two in Crisium considered for a geophysical network mission. My map shows both network candidate sites. The Picard site (A, B) was dropped and a site near a volcanic cone called Mons Latreille (C, D) was chosen. A hazard-free site nearby was selected via several studies in 2021-2022 (E-G). Tomorrow: the VIPER site.

Non-negative solutions of a sublinear elliptic problem
Juli\'an L\'opez-G\'omez, Paul H. Rabinowitz, Fabio Zanolin
https://arxiv.org/abs/2403.04396

Non-negative solutions of a sublinear elliptic problem
In this paper the existence of solutions, $(λ,u)$, of the problem $$-Δu=λu -a(x)|u|^{p-1}u \quad \hbox{in }Ω, \qquad u=0 \quad \hbox{on}\;\;\partialΩ,$$ is explored for $0 < p < 1$. When $p>1$, it is known that there is an unbounded component of such solutions bifurcating from $(σ_1, 0)$, where $σ_1$ is the smallest eigenvalue of $-Δ$ in $Ω$ under Dirichlet boundary conditions on $\partialΩ$. These solutions have $u \in P$, the interior of the positive cone. The continuati…

Anisotropic Hall effects in Bi$_2$Se$_3$/EuS interfaces
Juhi Singh, Karthik V. Raman, Narayan Mohanta
https://arxiv.org/abs/2403.04533 https://

Anisotropic Hall effects in Bi$_2$Se$_3$/EuS interfaces
Proximity coupling of ferromagnetic insulator EuS to the topological insulator Bi$_2$Se$_3$ has been proposed to break time-reversal symmetry near the surface of Bi$_2$Se$_3$, introducing an energy gap or a tilt in the surface Dirac cone. As an inverse proximity effect, strong spin-orbit coupling available in the topological surface states can enhance the Curie temperature of ferromagnetism in EuS largely beyond its bulk value, and also generate a magnetic anisotropy. This can result in a canti…

More good news from The David Suzuki Foundation
#Coffee grounds could improve farm grounds
People drink a lot of coffee, and some of the six million tonnes of grounds discarded annually into landfills can generate climate-altering methane and carbon dioxide. A study in the Journal of Chemical Technology and Biotechnology finds the grounds could be used to address agricultural contamination. <…

On generators of $k$-PSD closures of the positive semidefinite cone
Avinash Bhardwaj, Vishnu Narayanan, Abhishek Pathapati
https://arxiv.org/abs/2405.01208

On generators of $k$-PSD closures of the positive semidefinite cone
Positive semidefinite (PSD) cone is the cone of positive semidefinite matrices, and is the object of interest in semidefinite programming (SDP). A computational efficient approximation of the PSD cone is the $k$-PSD closure, $1 \leq k < n$, cone of $n\times n$ real symmetric matrices such that all of their $k\times k$ principal submatrices are positive semidefinite. For $k=1$, one obtains a polyhedral approximation, while $k=2$ yields a second order conic (SOC) approximation of the PSD cone. Th…

This https://arxiv.org/abs/2312.16463 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Cone Holography with Neumann Boundary Conditions and Brane-localized Gauge Fields
Cone holography is a codimension-$n$ doubly holographic model, which can be interpreted as the holographic dual of edge modes on defects. The initial model of cone holography is based on mixed boundary conditions. This paper formulates cone holography with Neumann boundary conditions, where the brane-localized gauge fields play an essential role. Firstly, we illustrate the main ideas in an AdS$_4$/CFT$_1$ toy model. We show that the $U(1)$ gauge field on the end-of-the-world brane can make the …

This https://arxiv.org/abs/2106.12623 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cubic color charge correlator in a proton made of three quarks and a gluon
The three point correlation function of color charge densities is evaluated explicitly in light cone gauge for a proton on the light cone. This includes both $C$-conjugation even and odd contributions. We account for perturbative corrections to the three-quark light cone wave function due to the emission of an internal gluon which is not required to be soft. We verify the Ward identity as well as the cancellation of UV divergences in the sum of all diagrams so that the correlator is independent…

Space is wild (Cone nebula region, Hydrogen alpha wavelengths, stars removed)
#astrophotography

This https://arxiv.org/abs/2312.03537 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Analysis on the cone of discrete Radon measures
We study analysis on the cone of discrete Radon measures over a locally compact Polish space $X$. We discuss probability measures on the cone and the corresponding correlation measures and correlation functions on the sub-cone of finite discrete Radon measures over $X$. For this, we consider on the cone an analogue of the harmonic analysis on the configuration space developed in [12]. We also study elements of the difference calculus on the cone: we introduce discrete birth-and-death gradients …

#TIL Our rod cells (the monochromatic photoreceptors) are apparently a little bit sensitive to cyan light. Good to know considering my cone cells skipped that area lol.
Could this be related to cyan being the most abundant in sunlight so we evolved to be less sensitive to it?
#askScience

Solutions to ${\rm SU}(n 1)$ Toda system with cone singularities via toric curves on compact Riemann surfaces
Jingyu Mu, Yiqian Shi, Bin Xu
https://arxiv.org/abs/2405.03161

Solutions to ${\rm SU}(n+1)$ Toda system with cone singularities via toric curves on compact Riemann surfaces
On a compact Riemann surface (X) with finite punctures (P_1, \ldots, P_k), we define toric curves as multi-valued, totally unramified holomorphic maps to (\mathbb{P}^n) with monodromy in a maximal torus of ({\rm PSU}(n+1)). \textit{Toric solutions} for the ({\rm SU}(n+1)) system on $X\setminus\{P_1,\ldots, P_k\}$ are recognized by their associated {\it toric} curves in (\mathbb{P}^n). We introduce a character n-ensemble as an (n)-tuple of meromorphic one-forms with simple poles and purely imagi…

This https://arxiv.org/abs/2401.14217 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

The explicit form of the unitary representation of the Poincaré group for vector-valued wave functions (massive and massless), with applications to photon's localization and position operators
We geometrically derive the explicit form of the Unitary representation of the Poincare group and use it to apply speed-of-light boosts to simple polarization basis to end up with Hawton-Baylis photon position operator with commuting components. We give explicit formulas for other photon boost eigenmodes. We investigate the underlying affine connections on the light cone in momentum space and find that while Pryce connection is metric semi-symmetric, the flat Hawton-Baylis connection is not sem…

This https://arxiv.org/abs/2402.16707 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Bondi-Hoyle-Lyttleton Accretion around the Rotating Hairy Horndeski Black Hole
We model the dynamical changes of the disk and shock cone resulting from the interaction of matter with the Horndeski black hole, at where the scalar field and spacetime has a strong interaction. The effects of the scalar hair, the black hole rotation parameter, and the impacts of the asymptotic speed have been examined, revealing the influence of these parameters on the shock cone and the trapped QPO modes within the cone. Numerical calculations have shown that the hair paramete significantly …

Exclusive production of double light neutral mesons at the $e^ e^-$ colliders
Junliang Lu, Cai-Ping Jia, Yu Jia, Xiaonu Xiong
https://arxiv.org/abs/2403.04762

Exclusive production of double light neutral mesons at the $e^+e^-$ colliders
In this work we investigate the exclusive production of a pair of light neutral mesons in $e^+e^-$ annihilation, where the final state bears an even $C$-parity. The production processes can be initiated via the photon fragmentation or the non-fragmentation mechanism. While the fragmentation contribution can be rigorously accounted, the non-fragmentation contributions are calculated within the framework of collinear factorization, where only the leading-twist light-cone distribution amplitudes (…

Spare a thought for this poor little one tonight. He had a lump removed from his leg today. It’s breaking my heart to see him like this.

This https://arxiv.org/abs/2309.01898 has been replaced.
link: https://scholar.google.com/scholar?q=a

Safe Legged Locomotion using Collision Cone Control Barrier Functions (C3BFs)
Legged robots exhibit significant potential across diverse applications, including but not limited to hazardous environment search and rescue missions and the exploration of unexplored regions both on Earth and in outer space. However, the successful navigation of these robots in dynamic environments heavily hinges on the implementation of efficient collision avoidance techniques. In this research paper, we employ Collision Cone Control Barrier Functions (C3BF) to ensure the secure movement of …

This https://arxiv.org/abs/2310.04176 has been replaced.
link: https://scholar.google.com/scholar?q=a

Approximating the set of Nash equilibria for convex games
In Feinstein and Rudloff (2023), it was shown that the set of Nash equilibria for any non-cooperative $N$ player game coincides with the set of Pareto optimal points of a certain vector optimization problem with non-convex ordering cone. To avoid dealing with a non-convex ordering cone, an equivalent characterization of the set of Nash equilibria as the intersection of the Pareto optimal points of $N$ multi-objective problems (i.e.\ with the natural ordering cone) is proven. So far, algorithms …

Tropical pseudostable curves
Renzo Cavalieri, Steffen Marcus, Jonathan Wise
https://arxiv.org/abs/2404.02654 https://arxiv.org/pdf/24…

Tropical pseudostable curves
We study the tropical version of the contraction morphism $\mathcal{T}$ between moduli spaces of stable and pseudostable curves. By promoting $\mathcal{T}$ to a logarithmic morphism, we obtain a piecewise linear function between the generalized cone complexes parameterizing tropical stable and pseudostable curves. The ray corresponding to the contracted divisor $δ_1$ is not contracted to the cone point but mapped onto a ray of $\mathcal{M}_{g,n}^{{\rm trop}, {\rm ps}}$, with a slope reflecting…

Martin boundary of a space-time Brownian motion with drift killed at the boundary of a moving cone
Sandro Franceschi
https://arxiv.org/abs/2404.16679 https…

Martin boundary of a space-time Brownian motion with drift killed at the boundary of a moving cone
We study a space-time Brownian motion with drift B(t)=(t_0+t,y_0+W(t)+t) killed at the moving boundary of the cone {(t,x):0

This https://arxiv.org/abs/2311.08073 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

$δN$ formalism on the past light-cone
We apply the gradient expansion approximation to the light-cone gauge, obtaining a separate universe picture at non-linear order in perturbation theory within this framework. Thereafter, we use it to generalize the $δN$ formalism in terms of light-cone perturbations. As a consistency check, we demonstrate the conservation of the gauge invariant curvature perturbation on uniform density hypersurface $ζ$ at the completely non-linear level. The approach studied provides a self-consistent framewo…

This https://arxiv.org/abs/2312.01807 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Moduli Space of Dihedral Spherical Surfaces and Measured Foliations
Cone spherical surfaces are orientable Riemannian surfaces with constant curvature one and a finite set of conical singularities. A subset of these surfaces, referred to as dihedral surfaces, is characterized by their monodromy groups, which notably preserve a pair of antipodal points on the unit two-sphere within three-dimensional Euclidean space. On each dihedral surface, we define a pair of transverse measured foliations that, in turn, comprehensively characterize the original dihedral surfa…

Dirac fermions collimation in heterostructures based on tilted Dirac cone materials
Ej Bou\^azzaoui Choubabi, Bouchaib Lemaalem, Mohamed Raggui, Abdelhadi Belouad, Rachid Hou\c{c}a, Abdellatif Kamal, Mohamed Monkade
https://arxiv.org/abs/2404.02485

Dirac fermions collimation in heterostructures based on tilted Dirac cone materials
This paper aims to theoretically analyze the behavior of Dirac fermions in tilted Dirac cone material, particularly those that have diffused a barrier potential.Our results show that the degree of tilt in the y-direction can lead to different collimations of the Dirac fermion beams relative to the Fermi and confinement surfaces. To study the transmission probability, we exploited our results numerically, taking into account the various configurations of the system and the different external and…

This https://arxiv.org/abs/2306.17328 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Einstein metrics from the Calabi ansatz via Derdziński duality
Drawing on results of Derdziński's from the 80's, we classify conformally Kähler, $U(2)$-invariant, Einstein metrics on the total space of $\mathcal{O}(-m)$, for all $m \in \mathbb{N}$. This yields infinitely many $1$-parameter families of metrics exhibiting several different behaviours including asymptotically hyperbolic metrics (more specifically of Poincaré type), ALF metrics, and metrics which compactify to a Hirzebruch surface $\mathbb{H}_m$ with a cone singularity along the "divisor at…

"The safety of all road users is a top priority for Waymo, and we look forward to learning from this unique event," says company whose defective robotaxi drove two blocks at fairly high speed on the wrong side of the road. They could've killed someone and it's a fun learning opportunity for them. #Robotaxis suck. Cone them.

A geometric characterisation of real C*-algebras
Cho-Ho Chu
https://arxiv.org/abs/2403.12628 https://arxiv.org/pdf/2403.12628<…

A geometric characterisation of real C*-algebras
We characterise the positive cone of a real C*-algebra geometrically. Given an open cone $Ω$ in a real Banach space $V$, with closure $\overline Ω$, we show that $Ω$ is the interior of the positive cone of a unital real C*-algebra if and only if it is a Finsler symmetric cone with an orientable extension, which is equivalent to the condition that $V$ is, in an equivalent norm, the hermitian part of a unital real C*-algebra with positive cone $\overlineΩ$.

This https://arxiv.org/abs/2311.07746 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Short Introduction to the Analysis on Manifolds with Conical Singularities
These notes recall central elements of the cone calculus. The focus lies on conically degenerate differential operators and the Laplace-Beltrami operator with respect to a conically degenerate metric as a prototypical example. The topics include manifolds with conical singularities, the Mellin transform, cone Sobolev spaces, and the notion of ellipticity in terms of the invertibility of the principal pseudodifferential symbol and the principal Mellin symbol. The notes end with a sketch the full…

This https://arxiv.org/abs/2212.02606 has been replaced.
link: https://scholar.google.com/scholar?q=a

Iterated Mapping Cones on the Koszul Complex and Their Application to Complete Intersection Rings
Let $(R,\mathfrak m, \mathsf k)$ be a complete intersection local ring, $K$ be the Koszul complex on a minimal set of generators of $\mathfrak m$, and $A=H(K)$ be its homology algebra. We establish exact sequences involving direct sums of the components of $A$ and express the images of the maps of these sequences as homologies of iterated mapping cones built on $K$. As an application of this iterated mapping cone construction, we recover a minimal free resolution of the residue field $\mathsf k…

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

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

This https://arxiv.org/abs/2404.08548 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Qubit frugal entanglement determination with the deep multi-scale entanglement renormalization ansatz
We study the deep multi-scale entanglement renormalization ansatz (DMERA) on quantum hardware and the causal cone of a subset of the qubits which make up the ansatz. This causal cone spans $O(M+\log{N})$ physical qubits on a quantum device, where $M$ and $N$ are the subset size and the total number qubits in the ansatz respectively. This allows for the determination of the von Neumann entanglement entropy of the $N$ qubit wave-function using $O(M+\log{N})$ qubits by diagonalization of the reduc…

There's a trolley problem party game.
Academic parties will never be the same.
#AcademicChatter #Ethics #Philosophy

Boundedness of log Fano cone singularities and discreteness of local volumes
Chenyang Xu, Ziquan Zhuang
https://arxiv.org/abs/2404.17134 https://

Boundedness of log Fano cone singularities and discreteness of local volumes
We prove that in any fixed dimension, K-semistable log Fano cone singularities whose volumes are bounded from below by a fixed positive number form a bounded set. As a consequence, we show that the set of local volumes of klt singularities of a fixed dimension has zero as the only accumulation point.

Tonight's dessert: coffee gelato in a waffle cone. Yum!

Properties of the complementarity set for the cone of copositive matrices
O. I. Kostyukova
https://arxiv.org/abs/2404.17375 https://a…

Properties of the complementarity set for the cone of copositive matrices
For a proper cone $K$ and its dual cone $K^*$ in $\mathbb R^n$, the complementarity set of $K$ is defined as ${\mathbb C}(K)=\{(x,y): x\in K,\; y\in K^*,\, x^\top y=0\}$. It is known that ${\mathbb C}(K)$ is an $n$-dimensional manifold in the space $\mathbb R^{2n}$. If $ K$ is a symmetric cone, points in ${\mathbb C}(K)$ must satisfy at least $n$ linearly independent bi-linear identities. Since this knowledge comes in handy when optimizing over such cones, it makes sense to search for similar…

Series C, Episode 11 - Moloch
ZEN: All systems functioning normally.
AVON: All right. Automatic controls, stabilize, and give us a scan in a cone of sixty degrees.
https://blake.torpidity.net/s/311/66 📺 B7B8

Bondi-Hoyle-Lyttleton Accretion around the Rotating Hairy Horndeski Black Hole
Orhan Donmez
https://arxiv.org/abs/2402.16707 https://…

Bondi-Hoyle-Lyttleton Accretion around the Rotating Hairy Horndeski Black Hole
We model the dynamical changes of the disk and shock cone resulting from the interaction of matter with the Horndeski black hole, at where the scalar field and spacetime has a strong interaction. The effects of the scalar hair, the black hole rotation parameter, and the impacts of the asymptotic speed have been examined, revealing the influence of these parameters on the shock cone and the trapped QPO modes within the cone. Numerical calculations have shown that the hair paramete significantly …

This https://arxiv.org/abs/2306.09142 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

GN-z11: The environment of an AGN at $z=$10.603
Recent observations with the \textit{James Webb} Space Telescope (JWST) have further refined the spectroscopic redshift of GN-z11, one of the most distant galaxies identified with the \textit{Hubble} Space Telescope (HST) at $z=10.603$. The presence of extremely dense gas ($>10^{10}$ cm$^{-3}$), the detection of high-ionisation lines and of CII*1335 emission, as well as the presence of an ionisation cone, indicate that GN-z11 also hosts an Active Galactic Nucleus (AGN). Further photometric and …

#Costco has #Lego kits for some very complex objects and has some assembled ones on display at warehouses. See them in person if you can. 🤯
Taking pics was tricky w the objects being inside plastic cases, reflections from lights around,...but I did my best, and cleaned up the images after.
1. &quo…

Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction
K. Aditya Mohan, Massimiliano Ferrucci, Chuck Divin, Garrett A. Stevenson, Hyojin Kim
https://arxiv.org/abs/2404.19075 https://arxiv.org/pdf/2404.19075
arXiv:2404.19075v1 Announce Type: new
Abstract: 4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an extremely ill-posed inverse problem. Existing approaches assume that the object remains static for the duration of several tens or hundreds of X-ray projection measurement images (reconstruction of consecutive limited-angle CT scans). However, this is an unrealistic assumption for many in-situ experiments that causes spurious artifacts and inaccurate morphological reconstructions of the object. To solve this problem, we propose to perform a 4D time-space reconstruction using a distributed implicit neural representation (DINR) network that is trained using a novel distributed stochastic training algorithm. Our DINR network learns to reconstruct the object at its output by iterative optimization of its network parameters such that the measured projection images best match the output of the CT forward measurement model. We use a continuous time and space forward measurement model that is a function of the DINR outputs at a sparsely sampled set of continuous valued object coordinates. Unlike existing state-of-the-art neural representation architectures that forward and back propagate through dense voxel grids that sample the object's entire time-space coordinates, we only propagate through the DINR at a small subset of object coordinates in each iteration resulting in an order-of-magnitude reduction in memory and compute for training. DINR leverages distributed computation across several compute nodes and GPUs to produce high-fidelity 4D time-space reconstructions even for extremely large CT data sizes. We use both simulated parallel-beam and experimental cone-beam X-ray CT datasets to demonstrate the superior performance of our approach.

This https://arxiv.org/abs/2303.06392 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonlinear Strict Cone Separation Theorems in Real Normed Spaces
In this paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric separation approach developed by Kasimbeyli (2010, SIAM J. Optim. 20), which is based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Compared to Kasimbeyli's separation theorem, we formulate our theorems for the separation of two cones under …

Exact and Approximate High-Multiplicity Scheduling on Identical Machines
Klaus Jansen, Kai Kahler, Esther Zwanger
https://arxiv.org/abs/2404.17274 https://…

Exact and Approximate High-Multiplicity Scheduling on Identical Machines
Goemans and Rothvoss (SODA'14) gave a framework for solving problems in time $enc(P)^{2^{O(N)}}enc(Q)^{O(1)}$ that can be described as finding a point in $\text{int.cone}(P\cap\mathbb{Z}^N)\cap Q$, where $P,Q\subset\mathbb{R}^N$ are (bounded) polyhedra. This framework can be used to solve various scheduling problems, but the encoding length $enc(P)$ usually involves large parameters like the makespan. We describe three tools to improve the framework by Goemans and Rothvoss: Problem-specific pre…

Apollonian carpets and the boundary of the Kahler cone of a hyperkahler manifold
Ekaterina Amerik, Andrey Soldatenkov, Misha Verbitsky
https://arxiv.org/abs/2402.11697

Apollonian carpets and the boundary of the Kahler cone of a hyperkahler manifold
The ample cone of a compact Kahler $n$-manifold $M$ is the intersection of its Kahler cone and the real subspace generated by integer (1,1)-classes. Its isotropic boundary is the set of all points $η$ on its boundary such that $\int_M η^n=0$. We are interested in the relation between the shape of the isotropic boundary of the ample cone of a hyperkahler manifold and the dynamics of its holomorphic automorphism group $G$. In this case, the projectivization of the ample cone is realized as an o…

Utilizing U-Net Architectures with Auxiliary Information for Scatter Correction in CBCT Across Different Field-of-View Settings
Harshit Agrawal, Ari Hietanen, Simo S\"arkk\"a
https://arxiv.org/abs/2402.17397

Utilizing U-Net Architectures with Auxiliary Information for Scatter Correction in CBCT Across Different Field-of-View Settings
Cone-beam computed tomography (CBCT) has become a vital imaging technique in various medical fields but scatter artifacts are a major limitation in CBCT scanning. This challenge is exacerbated by the use of large flat panel 2D detectors. The scatter-to-primary ratio increases significantly with the increase in the size of FOV being scanned. Several deep learning methods, particularly U-Net architectures, have shown promising capabilities in estimating the scatter directly from the CBCT projecti…

forgot a word so badly microsoft copilot had to diss me for it

This text message made me laugh. (Rehoboth is one of the beaches nearest to me. We go there a couple of times a year anyway. Sometimes even on the same weekends as the Bidens.)

Brock Bowers NFL Draft 2024: Combine Results, Scouting Report For Las Vegas Raiders TE https://www.yardbarker.com/nfl/articles/brock_bowers_nfl_draft_2024_combine_results_scouting_report_for_l…

Brock Bowers NFL Draft 2024: Combine Results, Scouting Report For Las Vegas Raiders TE
The 2024 NFL Draft is here, making it an excellent time to highlight some of the class' best players with scouting reports. Each report will include strengths, weaknesses and background information.  Here's our report on Brock Bowers. Height: 6'3'' Weight: 243 lbs 40-Time: DNP (Did Not Participate) 10-Yard Split: DNP Vertical: DNP Broad Jump: DNP 3-Cone: DNP Shuttle: DNP Explosive off the line of scrimmage into his routes then smooth and fluid through his vertical stem. Moves more like a big W…

This https://arxiv.org/abs/2306.04264 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Integer Carathéodory results with bounded multiplicity
The integer Carathéodory rank of a pointed rational cone $C$ is the smallest number $k$ such that every integer vector contained in $C$ is an integral non-negative combination of at most $k$ Hilbert basis elements. We investigate the integer Carathéodory rank of simplicial cones with respect to their multiplicity, i.e., the determinant of the integral generators of the cone. One of the main results states that simplicial cones with multiplicity bounded by five have the integral Carathéodory …

This https://arxiv.org/abs/2312.12084 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Differentiability of Adelic Volumes and Equidistribution on Quasi-Projective Varieties
Differentiability of geometric and arithmetic volumes of Hermitian line-bundles leads to the proof of equidistribution results on projective varieties using the variational principle. In this article, we work in the setting of adelic divisors on quasi-projective varieties recently introduced by Xinyi Yuan and Shou-Wu Zhang to show that their geometric and arithmetic adelic volume functions are differentiable on the big cone. We introduce the notions of positive intersection products and show th…

Hybrid Feedback Control for Global and Optimal Safe Navigation
Ishak Cheniouni, Soulaimane Berkane, Abdelhamid Tayebi
https://arxiv.org/abs/2402.17038 http…

Hybrid Feedback Control for Global and Optimal Safe Navigation
We propose a hybrid feedback control strategy that safely steers a point-mass robot to a target location optimally from all initial conditions in the n-dimensional Euclidean space with a single spherical obstacle. The robot moves straight to the target when it has a clear line-of-sight to the target location. Otherwise, it engages in an optimal obstacle avoidance maneuver via the shortest path inside the cone enclosing the obstacle and having the robot's position as a vertex. The switching stra…

guys its happening.. they are taking over my college, next step is the world
#LifeInCanada

Characterization of the attractor for nonautonomous reaction-diffusion equations with discontinuous nonlinearity
Jos\'e Valero
https://arxiv.org/abs/2405.01894

Characterization of the attractor for nonautonomous reaction-diffusion equations with discontinuous nonlinearity
In this paper, we study the asymptotic behavior of the solutions of a nonautonomous differential inclusion modeling a reaction-diffusion equation with a discontinuous nonlinearity. We obtain first several properties concerning the uniqueness and regularity of non-negative solutions. Then we study the structure of the pullback attractor in the positive cone, showing that it consists of the zero solution, the unique positive nonautonomous equilibrium and the heteroclinic connections between them,…

The mapping cone of an Eisenbud operator and applications to exact zero divisors
Liana M. \c{S}ega, Deepak Sireeshan
https://arxiv.org/abs/2403.12458 https…

The mapping cone of an Eisenbud operator and applications to exact zero divisors
Let $(Q,\mathfrak{m},{\sf k})$ be a local ring that admits an exact pair of zero divisors $(f,g)$, $M$ a $Q$-module with $fM = 0$ and $U$ a free resolution of $M$ over $Q$. We construct a degree $-2$ chain map, which we call an Einsenbud operator, on the complex $U \otimes_Q Q/(f,g)$ and use the mapping cone of the operator to study two exact sequences that relate homology over $Q$ to homology over $Q/(f)$. Several applications are given.

Road Scenes, April 2024.
#ShittyCameraChallenge #photo #photography

An improved light-cone harmonic oscillator model for the $\phi$-meson longitudinal leading-twist light-cone distribution amplitude
Dan-Dan Hu, Xing-Gang Wu, Long Zeng, Hai-Bing Fu, Tao Zhong
https://arxiv.org/abs/2403.10003

An improved light-cone harmonic oscillator model for the $ϕ$-meson longitudinal leading-twist light-cone distribution amplitude
In the present paper, we study the properties of $ϕ$-meson longitudinal leading-twist light-cone distribution amplitude $ϕ_{2;ϕ}^{\|}(x,μ)$ by starting from a light-cone harmonic oscillator model for its wavefunction. To fix the input parameters, we derive the first ten $ξ$-moments of $ϕ_{2;ϕ}^{\|}(x,μ)$ by using the QCD sum rules approach under the background field theory. The shape of $ϕ_{2;ϕ}^{\|}(x,μ=2~{\rm GeV})$ tends to be a single-peak behavior, which is consis…

This https://arxiv.org/abs/2311.08787 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Polygonal Cone Control Barrier Functions (PolyC2BF) for safe navigation in cluttered environments
In fields such as mining, search and rescue, and archaeological exploration, ensuring real-time, collision-free navigation of robots in confined, cluttered environments is imperative. Despite the value of established path planning algorithms, they often face challenges in convergence rates and handling dynamic infeasibilities. Alternative techniques like collision cones struggle to accurately represent complex obstacle geometries. This paper introduces a novel category of control barrier functi…

Series C, Episode 11 - Moloch
ZEN: All systems functioning normally.
AVON: All right. Automatic controls, stabilize, and give us a scan in a cone of sixty degrees.
https://blake.torpidity.net/s/311/66 📺 B7B8

This https://arxiv.org/abs/2306.09142 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

GN-z11: The environment of an AGN at $z=$10.603
Recent observations with the \textit{James Webb} Space Telescope (JWST) have further refined the spectroscopic redshift of GN-z11, one of the most distant galaxies identified with the \textit{Hubble} Space Telescope (HST) at $z=10.603$. The presence of extremely dense gas ($>10^{10}$ cm$^{-3}$), the detection of high-ionisation lines and of CII*1335 emission, as well as the presence of an ionisation cone, indicate that GN-z11 also hosts an Active Galactic Nucleus (AGN). Further photometric and …

This https://arxiv.org/abs/2403.07365 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

On exactly solvable Yang-Baxter models and enhanced symmetries
We study Yang-Baxter deformations of the flat space string that result in exactly solvable models, finding the Nappi-Witten model and its higher dimensional generalizations. We then consider the spectra of these models obtained by canonical quantization in light-cone gauge, and match them with an integrability-based Bethe ansatz approach. By considering a generalized light-cone gauge we can describe the model by a nontrivially Drinfel'd twisted S matrix, explicitly verifying the twisted structu…

Double extension of flat pseudo-Riemannian $F$-Lie algebras
Alexander Torres-Gomez, Fabricio Valencia
https://arxiv.org/abs/2405.02130 https://

Double extension of flat pseudo-Riemannian $F$-Lie algebras
We define the concept of a flat pseudo-Riemannian $F$-Lie algebra and construct its corresponding double extension. This algebraic structure can be interpreted as the infinitesimal analogue of a Frobenius Lie group devoid of Euler vector fields. We show that the double extension provides a framework for generating all weakly flat Lorentzian non-abelian bi-nilpotent $F$-Lie algebras possessing one dimensional light-cone subspaces. A similar result can be established for nilpotent Lie algebras eq…

This https://arxiv.org/abs/2303.06392 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonlinear Strict Cone Separation Theorems in Real Normed Spaces
In this paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric separation approach developed by Kasimbeyli (2010, SIAM J. Optim. 20), which is based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Compared to Kasimbeyli's separation theorem, we formulate our theorems for the separation of two cones under …

Hub Network Design Problem with Capacity, Congestion and Heterogeneous Economies of Scale
Xiaotong Liu
https://arxiv.org/abs/2404.03521 https://

Hub Network Design Problem with Capacity, Congestion and Heterogeneous Economies of Scale
We propose a joint model that links the strategic level location and capacity decisions with the operational level routing and hub assignment decisions to solve hub network design problem with congestion and heterogeneous economics of scale. We also develop a novel flow-based mixed-integer second-order cone programming (MISOCP) formulation. We perform numerical experiments on a real-world data set to validate the efficiency of solving the MISOCP reformulation. The numerical studies yield observ…

This https://arxiv.org/abs/2402.11697 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Apollonian carpets and the boundary of the Kahler cone of a hyperkahler manifold
The ample cone of a compact Kahler $n$-manifold $M$ is the intersection of its Kahler cone and the real subspace generated by integer (1,1)-classes. Its isotropic boundary is the set of all points $η$ on its boundary such that $\int_M η^n=0$. We are interested in the relation between the shape of the isotropic boundary of the ample cone of a hyperkahler manifold and the dynamics of its holomorphic automorphism group $G$. In this case, the projectivization of the ample cone is realized as an o…

This https://arxiv.org/abs/2309.12155 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A four-term exact sequence of surface orbifold pure braid groups
We prove a four-term exact sequence of surface orbifold pure braid groups for all genus $\geq 1$, $2$-dimensional orientable orbifolds with cone points. This corrects our earlier result in arXiv.2106.08110.

Frobenius light cone and the shift unitary
Chao Yin, Andrew Lucas, David T. Stephen
https://arxiv.org/abs/2402.07990 https://arxiv.or…

Frobenius light cone and the shift unitary
We bound the time necessary to implement the shift unitary on a one-dimensional ring, both using local Hamiltonians and those with power-law interactions. This time is constrained by the Frobenius light cone; hence we prove that shift unitaries are parametrically harder to implement than preparing long-range Bell pairs for sufficiently small power-law exponent. We note an intriguing similarity between the proof of our results, and the hardness of preparing symmetry-protected topological states …

On the penalization by the perimeter in shape optimization applied to Dirichlet inverse obstacle problem
Fabien Caubet, Marc Dambrine, J\'er\'emi Dard\'e
https://arxiv.org/abs/2404.03536

On the penalization by the perimeter in shape optimization applied to Dirichlet inverse obstacle problem
This paper is devoted to the understanding of regularisation process in the shape optimization approach to the so-called Dirichlet inverse obstacle problem for elliptic operators. More precisely, we study two different regularisations of the very classical shape optimization approach consisting in minimizing a mismatched functional. The first one is an implicit regularisation when working in the class of inclusion having a uniform $\varepsilon$-cone property, a natural class in shape optimizati…

This https://arxiv.org/abs/2402.11982 has been replaced.
initial toot: https://mastoxiv.page/@a…

Non-magnetic layers with a single Dirac cone at high-symmetry point of the Brillouin zone
It is well known that a single Dirac cone at high-symmetry point (HSP) of a Brillouin zone, akin to the one in graphenes' band structure, can not appear as the only quasiparticle at the Fermi level in two-dimensional (2D), non-magnetic materials. Here we found two layer groups with time-reversal symmetry, among all possible both without- and with spin-orbit coupling, that host one Dirac cone at HSP and we show which additional dispersions appear: a pair of Dirac lines on opposite BZ edges and a…

Regularities for solutions to the $L_p$ dual Minkowski problem for unbounded closed sets
Li Chen, Qiang Tu
https://arxiv.org/abs/2403.00651 https://…

Regularities for solutions to the $L_p$ dual Minkowski problem for unbounded closed sets
Recently, the dual Minkowski problem for unbounded closed convex sets in a pointed closed convex cone was proposed and a weak solution to the corresponding Monge-Ampère equation is provided. In this paper, we consider the regularities of solutions to this problem. More generally, we consider the $L_p$ dual Minkowski problem for unbounded closed convex sets which amounts to solving a Dirichlet problem for a class of Monge-Ampère type equations. Our main purpose is to show the existence, regula…

The Kawamata-Morrison Cone Conjecture for Generalized Hyperelliptic Variety
Martina Monti, Ana Quedo
https://arxiv.org/abs/2403.13156 https://

The Kawamata-Morrison Cone Conjecture for Generalized Hyperelliptic Variety
A Generalized Hyperelliptic Variety (GHV) is the quotient of an abelian variety by a free action of a finite group which does not contain any translation. These varieties are natural generalizations of bi-elliptic surfaces. In this paper we prove the Kawamata-Morrison Cone Conjecture for these manifolds using the analogous results established by Prendergast-Smith for abelian varieties.

The volume of conformally flat manifolds as hypersurfaces in the light-cone
Riku Kishida
https://arxiv.org/abs/2404.14761 https://arx…

The volume of conformally flat manifolds as hypersurfaces in the light-cone
In this paper, we focus on a conformally flat Riemannian manifold $(M^n,g)$ of dimension $n$ isometrically immersed into the $(n+1)$-dimensional light-cone $Λ^{n+1}$ as a hypersurface. We compute the first and the second variational formulas on the volume of such hypersurfaces. Such a hypersurface $M^n$ is not only immersed in $Λ^{n+1}$ but also isometrically realized as a hypersurface of a certain null hypersurface $N^{n+1}$ in the Minkowski spacetime, which is different from $Λ^{n+1}$. Mor…

Sandpile groups for cones over trees
Victor Reiner, Dorian Smith
https://arxiv.org/abs/2402.15453 https://arxiv.org/pdf/2402.15453

Sandpile groups for cones over trees
Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex to a tree. For example, it is shown that the number of generators of the sandpile group is at most one less than the number of leaves in the tree. For trees on a fixed number of vertices, the paths and stars are shown to provide extreme behavior, not only for …

This https://arxiv.org/abs/2403.16191 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Unveiling the underlying structure of axial-vector bottom-charm tetraquarks in the light of their magnetic moments
The magnetic moment yields an excellent framework to explore the inner structure of particles determined by the quark-gluon dynamics of QCD, as it is the leading-order response of a bound system to a weak external magnetic field. Motivated by this, in this study, the magnetic moments of possible axial-vector $T_{bc\bar u \bar u}$, $T_{bc\bar d \bar d}$, and $T_{bc\bar u \bar d}$ tetraquarks are obtained with the help of light-cone QCD sum rules. For this purpose, we assume that these states are…

Analysis of Kernel Mirror Prox for Measure Optimization
Pavel Dvurechensky, Jia-Jie Zhu
https://arxiv.org/abs/2403.00147 https://arxi…

Analysis of Kernel Mirror Prox for Measure Optimization
By choosing a suitable function space as the dual to the non-negative measure cone, we study in a unified framework a class of functional saddle-point optimization problems, which we term the Mixed Functional Nash Equilibrium (MFNE), that underlies several existing machine learning algorithms, such as implicit generative models, distributionally robust optimization (DRO), and Wasserstein barycenters. We model the saddle-point optimization dynamics as an interacting Fisher-Rao-RKHS gradient flow…

This https://arxiv.org/abs/2403.03988 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

D6 branes wrapped on a spindle and $Y^{p,q}$ manifolds
We present new solutions of 8d gauged supergravity which, upon uplift to type IIA, represent D6 branes wrapped on spindles. A further circle uplift gives 11d supergravity on a Calabi-Yau three-fold which is the cone over five-dimensional $Y^{p,q}$ manifolds. This highlights a connection between co-homogeneity one Sasaki-Einstein metrics in general dimension and the recently introduced spindle solutions in gauged supergravity. We find that a similar connection also exists for the small resolutio…

The lattice structure of negative Sobolev and extrapolation spaces
Sahiba Arora, Jochen Gl\"uck, Felix L. Schwenninger
https://arxiv.org/abs/2404.02116

The lattice structure of negative Sobolev and extrapolation spaces
It is well-known that the Sobolev spaces $W^{k,p}(\mathbb R^d)$ are vector lattices with respect to the pointwise almost everywhere order if $k \in \{0,1\}$, but not if $k \ge 2$. In this note, we consider negative $k$ and show that the span of the positive cone in $W^{k,p}(\mathbb R^d)$ is a vector lattice in this case. We also prove a related abstract result: if $(T(t))_{t \in [0,\infty)}$ is a positive $C_0$-semigroup on a Banach lattice $X$ with order continuous norm, then the span of the…

This https://arxiv.org/abs/2402.11982 has been replaced.
initial toot: https://mastoxiv.page/@a…

Non-magnetic layers with a single Dirac cone at high-symmetry point of the Brillouin zone
It is well known that a single Dirac cone at high-symmetry point (HSP) of a Brillouin zone, akin to the one in graphenes' band structure, can not appear as the only quasiparticle at the Fermi level in two-dimensional (2D), non-magnetic materials. Here we found two layer groups with time-reversal symmetry, among all possible both without- and with spin-orbit coupling, that host one Dirac cone at HSP and we show which additional dispersions appear: a pair of Dirac lines on opposite BZ edges and a…

This https://arxiv.org/abs/2402.18901 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Revealing the nature of $Ω_{c}$-like states from pentaquark perspective
We systematically study the electromagnetic properties of controversial states whose internal structure is not elucidated and we try to offer a different point of view to unravel the internal structure of these states. Inspired by the $Ω_c$ states observed by the LHCb Collaboration, we study the electromagnetic properties of the $Ω_c$-like states as the compact diquark-diquark-antiquark pentaquarks with both $J^P = \frac{1}{2}^-$ and $J^P = \frac{3}{2}^-$ in the context of the QCD light-cone …

Exterior stability of Minkowski spacetime with borderline decay
Dawei Shen
https://arxiv.org/abs/2405.00735 https://arxiv.org/pdf/240…

Exterior stability of Minkowski spacetime with borderline decay
In 1993, the global stability of Minkowski spacetime has been proven in the celebrated work of Christodoulou and Klainerman \cite{Ch-Kl}. In 2003, Klainerman and Nicolò \cite{Kl-Ni} revisited Minkowski stability in the exterior of an outgoing null cone. In \cite{Shen23}, the author extended the results of \cite{Ch-Kl} to minimal decay assumptions. In this paper, we prove that the exterior stability of Minkowski holds with decay which is borderline compared to the minimal decay considered in \c…

This https://arxiv.org/abs/2310.04176 has been replaced.
link: https://scholar.google.com/scholar?q=a

Approximating the set of Nash equilibria for convex games
In Feinstein and Rudloff (2023), it was shown that the set of Nash equilibria for any non-cooperative $N$ player game coincides with the set of Pareto optimal points of a certain vector optimization problem with non-convex ordering cone. To avoid dealing with a non-convex ordering cone, an equivalent characterization of the set of Nash equilibria as the intersection of the Pareto optimal points of $N$ multi-objective problems (i.e.\ with the natural ordering cone) is proven. So far, algorithms …

Characterizing subadjoint varieties among Legendrian varieties
Jun-Muk Hwang
https://arxiv.org/abs/2404.19376 https://arxiv.org/pdf/2…

Characterizing subadjoint varieties among Legendrian varieties
For a symplectic vector space $V$, a projective subvariety $Z \subset {\bf P} V$ is a Legendrian variety if its affine cone $\widehat{Z} \subset V$ is Lagrangian. In addition to the classical examples of subadjoint varieties associated to simple Lie algebras, many examples of nonsingular Legendrian varieties have been discovered which have positive-dimensional automorphism groups. We give a characterization of subadjoint varieties among such Legendrian varieties in terms of the isotropy represe…

This https://arxiv.org/abs/2403.02764 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Unbalanced L1 optimal transport for vector valued measures and application to Full Waveform Inversion
Optimal transport has recently started to be successfully employed to define misfit or loss functions in inverse problems. However, it is a problem intrinsically defined for positive (probability) measures and therefore strategies are needed for its applications in more general settings of interest. In this paper we introduce an unbalanced optimal transport problem for vector valued measures starting from the $L^1$ optimal transport. By lifting data in a self-dual cone of a higher dimensional v…

This https://arxiv.org/abs/2404.12755 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Expanding Ricci solitons coming out of weakly PIC1 metric cones
Motivated by recent work of Deruelle-Schulze-Simon, we study complete weakly PIC1 Ricci flows with Euclidean volume growth coming out of metric cones. We show that such a Ricci flow must be an expanding gradient Ricci soliton, and as a consequence, any metric cone at infinity of a complete weakly PIC1 Kähler manifold with Euclidean volume growth is biholomorphic to complex Euclidean space in a canonical way.

The minimal exponent of cones over smooth complete intersection projective varieties
Qianyu Chen, Bradley Dirks, Mircea Musta\c{t}\u{a}
https://arxiv.org/abs/2404.18289

The minimal exponent of cones over smooth complete intersection projective varieties
We compute the minimal exponent of the affine cone over a complete intersection of smooth projective hypersurfaces intersecting transversely. The upper bound for the minimal exponent is proved, more generally, in the weighted homogeneous setting, while the lower bound is deduced from a general lower bound in terms of a strong factorizing resolution in the sense of Bravo and Villamayor.

The multiplicity of cyclic coverings of a singularity of an algebraic variety
Toya Kumagai, Tomohiro Okuma
https://arxiv.org/abs/2403.14355 https://…

The multiplicity of cyclic coverings of a singularity of an algebraic variety
Let $V$ be an affine algebraic variety, and let $p\in V$ be a singular point. For a regular function $g$ on $V$ such that $g(p)=0$ and for a positive integer $n$, we consider the cyclic covering $ϕ_n\: V_n \to V$ of degree $n$ branched along the hypersurface defined by $g$. We will prove that for sufficiently large $n$, the tangent cone of $V_n$ at $ϕ_n^{-1}(p)$ is, as an affine variety, the product of the tangent cone of the branch locus and the affine line. In particular, the multiplicity o…

Integer Points in Arbitrary Convex Cones: The Case of the PSD and SOC Cones
Jes\'us A. De Loera, Brittney Marsters, Luze Xu, Shixuan Zhang
https://arxiv.org/abs/2403.09927

Integer Points in Arbitrary Convex Cones: The Case of the PSD and SOC Cones
We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigroup associated with nonpolyhedral cones can sometimes have a notion of finite generating set. We show this is true for the cone of positive semidefinite matrices (PSD) and the second-order cone (SOC). Both cones have a finite generating set of integer points, similar in spirit to Hilbert bases, under the action of a f…

This https://arxiv.org/abs/2312.01141 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Moser's Bernstein Theorem
In this paper, we prove the following version of the famous Bernstein's theorem: Let $X\subset \mathbb R^{n+k}$ be a closed and connected set with Hausdorff dimension $n$. Assume that $X$ satisfies the monotonicity formula at $p\in X$. Then, the following statements are equivalent: (1) $X$ is an affine linear subspace; (2) $X$ is a definable set that is Lipschitz regular at infinity and its geometric tangent cone at infinity, $C(X,\infty)$, is a linear subspace; (3) $X$ is a definable set…

This https://arxiv.org/abs/2305.05637 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Signed tropicalization of polar cones
We study the tropical analogue of the notion of polar of a cone, working over the semiring of tropical numbers with signs. We characterize the cones which arise as polars of sets of tropically nonnegative vectors by an invariance property with respect to a tropical analogue of Fourier-Motzkin elimination. We also relate tropical polars with images by the nonarchimedean valuation of classical polars over real closed nonarchimedean fields and show, in particular, that for semi-algebraic sets over…

This https://arxiv.org/abs/2105.08419 has been replaced.
link: https://scholar.google.com/scholar?q=a

A sparse ADMM-based solver for linear MPC subject to terminal quadratic constraint
Model Predictive Control (MPC) typically includes a terminal constraint to guarantee stability of the closed-loop system under nominal conditions. In linear MPC this constraint is generally taken on a polyhedral set, leading to a quadratic optimization problem. However, the use of an ellipsoidal terminal constraint may be desirable, leading to an optimization problem with a quadratic constraint. In this case, the optimization problem can be solved using Second Order Cone (SOC) programming solve…

This https://arxiv.org/abs/2310.17229 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Geometry of exactness of moment-SOS relaxations for polynomial optimization
The moment-SOS (sum of squares) hierarchy is a powerful approach for solving globally non-convex polynomial optimization problems (POPs) at the price of solving a family of convex semidefinite optimization problems (called moment-SOS relaxations) of increasing size, controlled by an integer, the relaxation order. We say that a relaxation of a given order is exact if solving the relaxation actually solves the POP globally. In this note, we study the geometry of the exactness cone, defined as the…

Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations
Sergio I. Bugosen, Robert B. Parker, Carleton Coffrin
https://arxiv.org/abs/2404.17541 <…

Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations
We demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We conduct experiments on 36 cases from the PGLib-OPF library for two objective functions, (1) power generation maximization and (2) generation cost minimization. Significant optimality gap improvements are shown for the maximization problem, where the LNC strengthe…