Tootfinder

Reflexive graph lenses in univalent foundations
Jonathan Sterling
https://arxiv.org/abs/2404.07854 https://arxiv.org/pdf/2404.07854…

Reflexive graph lenses in univalent foundations
Martin-Löf's identity types provide a generic (albeit opaque) notion of identification or "equality" between any two elements of the same type, embodied in a canonical reflexive graph structure $(=_A, \mathbf{refl})$ on any type $A$. The miracle of Voevodsky's univalence principle is that it ensures, for essentially any naturally occurring structure in mathematics, that this the resultant notion of identification is equivalent to the type of isomorphisms in the category of such structures. Cha…

This https://arxiv.org/abs/2211.02603 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches
The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within $Λ$CDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observa…

Kiselman Minimum Principle and Rooftop Envelopes in Complex Hessian Equations
Per {\AA}hag, Rafa{\l} Czy\.z, Chinh H. Lu, Alexander Rashkovskii
https://arxiv.org/abs/2405.04948

Kiselman Minimum Principle and Rooftop Envelopes in Complex Hessian Equations
We initiate the study of $m$-subharmonic functions with respect to a semipositive $(1,1)$-form in Euclidean domains, providing a significant element in understanding geodesics within the context of complex Hessian equations. Based on the foundational Perron envelope construction, we prove a decomposition of $m$-subharmonic solutions, and a general comparison principle that effectively manages singular Hessian measures. Additionally, we establish a rooftop equality and an analogue of the Kiselma…

In short: "Biden bad, Trump worse"
RT @tribelaw (tw)
“Threatening to abandon Biden is an implicit promise to support Trump. Like it or not, we face a binary choice: democracy or tyranny, liberty or subjugation, dignity or degradation, equality or injustice, order or chaos.
No other election in our lifetime will demand that we make a choice between morality and depravity, but here we are. We should not threaten to support depravity, even indirectly, as a pressure …

This https://arxiv.org/abs/2208.11551 has been replaced.
link: https://scholar.google.com/scholar?q=a

PDE characterisation of geometric distribution functions and quantiles
We show that in any Euclidean space, an arbitrary probability measure can be reconstructed explicitly by its geometric (or spatial) distribution function. The reconstruction takes the form of a (potentially fractional) linear PDE, where the differential operator is given in closed form. This result implies that, contrary to a common belief in the statistical depth community, geometric cdf's in principle provide exact control over the probability content of all depth regions. We present a compre…

I've been reading Ray Dailo's "Principles for dealing with the changing world order" in which he charts the rise and fall of empires and kingdoms and dynasties.
The main cycle, he reckons is:
1) Winner of a war consolidates power, unites the population (often through oppression)
2) A smart cooperative equitable educated society with meritocracy means good societal progress and wide sharing of the wealth.
3) Long period of peace, building good tech and military and financial systems.
4) Leadership corrupts: Excessive debt, money-printing, inequality, financial ruin, no sense of solidarity, then a natural disaster pushes it over the edge
5) The fall: Escalating rebellions, very bad inequality, internal conflicts
6) Civil war, revolution, eventually a strong leader proves the winner and back to 1.
We in the western civilization are very clearly in the late states of this kind of cycle, and it's frankly terrifying with the weapons we have these days when it comes to a war.
The leadership is too corrupt to try and fix the inequality or invest in that well educated, equitable, cooperative society.
He explicitly agrees with Marx and implicitly with me a lot more than I'd have expected from the rabid capitalist that Ray Dailo is.
It's interesting to hear his emphasis on inequality and how a prosperous society depends upon sharing the gains of prosperity widely. You tend to hear hyper-capitalists mostly emphasizing that capital's gains should go to capital, and Ray is certainly suggesting the opposite here. That if that happens, it corrupts the leadership and ends with cronyism and debt and revolution.
We seem to basically agree what creates good prosperous peaceful civil society, and that capitalism in the Anglican world isn't doing it, and that fucked up corrupt government is why we aren't doing it.
We'd offer fairly different prescriptions though I think.
#reading #books #economics

This https://arxiv.org/abs/2303.00953 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Construction of real algebraic functions with prescribed preimages
Nash and Tognoli show that smooth closed manifolds can be the zero sets of some real polynomial maps and non-singular. The canonical projections of spheres naturally embedded in the $1$-dimensional higher Euclidean spaces and some natural functions on projective spaces, Lie groups and their quotient spaces are important examples of real algebraic functions being also Morse. In general, it is difficult to construct such examples of maps and the structures of the manifolds. In addition the maps a…

Transnistria, the breakaway Moldovan province on Ukraine's Western border, has requested that Russia provide it with "defense" to protect its Russian residents. This is the same premise used to justify Russia's invasion of Ukraine's Donbas. A Russian military force on Ukraine's Western border would create a two-front war.
Russophile Republicans should recognize that any Russian buildup in Transnistria is certainly a prelude to a wider war.
**We must fund…

Exploring Text-based Realistic Building Facades Editing Applicaiton
Jing Wang, Xin Zhang
https://arxiv.org/abs/2405.02967 https://arx…

Exploring Text-based Realistic Building Facades Editing Applicaiton
This paper explores the utilization of diffusion models and textual guidance for achieving localized editing of building facades, addressing the escalating demand for sophisticated editing methodologies in architectural design and urban planning. Leveraging the robust generative capabilities of diffusion models, this study presents a promising avenue for realistically synthesizing and modifying architectural facades. Through iterative diffusion and text descriptions, these models adeptly captur…

Exploring Text-based Realistic Building Facades Editing Applicaiton
Jing Wang, Xin Zhang
https://arxiv.org/abs/2405.02967 https://arx…

Exploring Text-based Realistic Building Facades Editing Applicaiton
This paper explores the utilization of diffusion models and textual guidance for achieving localized editing of building facades, addressing the escalating demand for sophisticated editing methodologies in architectural design and urban planning. Leveraging the robust generative capabilities of diffusion models, this study presents a promising avenue for realistically synthesizing and modifying architectural facades. Through iterative diffusion and text descriptions, these models adeptly captur…