Research
Research
Research
Research
38,912+ open-access research outputs.
Degenerate quantum eigenspaces can support substantial changes in nodal geometry at fixed energy. We show that, for the two-dimensional isotropic harmonic oscillator, this restructuring is organized b…
Galaxy physical properties are influenced by their environments, but the processes responsible for mass and environmental quenching and structural transformations remain debated. Galaxy clusters are i…
We give a self-contained, modern exposition of \'Edouard Goursat's 1887 theorem on pseudo-elliptic integrals -- those integrals of the form $\int F(t)\,\d t/\sqrt{R(t)}$ with $R$ a cubic or quartic po…
We develop the ODE/IM correspondence for the higher-order Mathieu equation arising from the quantum Seiberg-Witten curve of the pure $SU(r+1)$ ${\cal N}=2$ supersymmetric Yang-Mills theory. From the s…
We develop a geometric and information-theoretic framework for encoder-decoder learning built on the Information Bottleneck (IB) principle. Recasting IB as a rate-distortion problem with Kullback-Leib…
The choice of loss function in classification involves a fundamental trade-off: smooth losses (like Cross-Entropy) enable fast optimization rates but yield slow square-root consistency bounds, while p…
Let $F$ be a finite field of odd characteristic. We prove that any set $A\subset F$ with $|A|\geq C|F|^{5/6}$ contains a nontrivial quadratic progression $(x, x+y, x+y^2), y\neq 0.$ For prime fields, …
An \'{e}tale space over a topological space $Y$ is defined as a local homeomorphism from a topological space $X$ into $Y$. They often come up in topos theory because of the equivalence between sheaves…
Let \((X,J,\omega)\) be a closed \(2n\)-dimensional almost K\"{a}hler manifold with negative sectional curvature. We prove that if the Nijenhuis tensor of the almost complex structure is sufficiently …
Context: Documenting Architectural Design Decisions (ADDs) is a critical factor in the software lifecycle, essential for efficient system maintenance, developer onboarding, and preventing knowledge va…
Let $G = \mathrm{SL}(n,\mathbb{C})$, let $B$ be a fixed Borel subgroup, and let $P \supset B$ be a parabolic subgroup determined by a composition $(c_1,\dots,c_k)$ of $n$. Write $P'$ for the derived g…
A recent construction of linear complementary pairs (LCPs) of algebraic geometry codes is intimately linked to the identification of non-special divisors of small degree within a function field over a…
The layered delafossite-like antiferromagnet AgCrSe$_2$ is a superionic conductor at high temperatures and has been reported to exhibit anomalous Hall behavior and Kondo physics at low temperatures. T…
We study stability theory in Hilbert spaces quantitatively. We prove that the inner product on the unit ball is $(k,\epsilon)$-stable for all $k\ge \exp(\pi/\epsilon)$, and it is not $(k,\epsilon)$-st…
In 2014, Michal Lewicki and Andrzej Olbry\'s proved that if a real valued function $f$ defined on the real line satisfies the conditional functional equation \[ f(tx + (1-t)y) = t f(x) + (1-t) f(y),\q…
Let $\mathcal{OP}_n$ be the monoid of all orientation-preserving full transformations on $X_n=\{1,\dots, n\}$ with the natural order. For $\alpha \in \mathcal{OP}_n$, let $F(\alpha)=\{y\in X_n: y\alph…
Let $\mathcal{PO}_n$ be the monoid of all order-preserving partial transformations on $X_n=\{1,\dots, n\}$ with the natural order, and let $\mathcal{O}_n$ and $\mathcal{POI}_n$ denote its submonoids o…
Low-frequency turbulence in the solar chromosphere remains poorly understood. We address 1) the sources of low-frequency turbulence that potentially heat the chromosphere, and 2) how turbulence is tra…
Using DFT+DMFT we study the normal-state electronic structure and magnetic correlations of the recently discovered alternating single-layer bilayer Raddlesden-Popper nickelate La$_5$Ni$_3$O$_{11}$ (12…
Differential abundances of C, O, Mg, Al, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Y, and Zr were determined from high signal-to-noise VLT/UVES spectra for 25 turnoff stars with -2.4 < [Fe/H] < -1.3. Eff…
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