Research
Research
Research
Research
68,362+ 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…
Barvinok introduced the symmetrized determinant ($\sdet$) as a \emph{non-commutative} analogue of the determinant. Intuitively, given a square matrix over an associative algebra, we can obtain the sym…
We present a highly simplified nonlinear hydrodynamical model to emulate the main observed features of amplitude modulation (commonly known as Blazhko effect) in RR Lyrae stars. The model is based on …
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 respond to the recent suggestion by A. Gal [arXiv:2604.18259] that the sharp pion-momentum peak at $p_{\pi^-} \approx 113.8$~MeV/$c$ observed in our $^7\mathrm{Li}(e,e^\prime K^+)$ electroproductio…
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…
Most service providers, such as Google, save logs from data generated by users while using the service. Many service providers provide users with privacy controls to manage whether, how, and for how l…
Mirror symmetry predicts an action by the fundamental group of a conjectural stringy K\"ahler moduli space on the derived category of an algebraic variety. For a toric variety, a model for this space …
Protecting sensitive health data while enabling collaborative analysis is a central challenge in healthcare. Traditional machine learning (ML) requires institutions to pool anonymized patient records,…
In natural language processing, the entropy of a language is a measure of its unpredictability and complexity. The first study on this subject was conducted by Claude Shannon in 1951. By having partic…
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…
A merger of clusters naturally drives shocks with Mach number $\mathscr{M}\lesssim 3$ in the intra-cluster medium (ICM). This process creates several distinct signatures, including sharp surface brigh…
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…
XRISM observations to date have shown that gas kinetic pressures in the intracluster medium (ICM) tend towards the low end of predictions from cosmological simulations. Here, we present a XRISM observ…
Free open-access publishing with Google Scholar indexing.
Submission Guide →