Research
Research
Research
Research
2,275+ open-access research outputs.
Since the dawn of Trading Card Games, the genre has grown into a multi-billion-dollar industry engaging millions of analog and digital players worldwide. Popular TCGs rely on regular updates, balance …
Let $k\ge 2$ be fixed integer, $0<c<1$ a constant. Consider a graph $G$ with $n$ vertices and average degree $cn$. We answer a question of Simon Griffiths by showing that $G$ has $k$ vertices such tha…
We demonstrate exponential quantum speedup for a restricted-Hamming-weight version of Simon's problem on present-day superconducting quantum processors by introducing a hardware-aware compilation stra…
Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topol…
We study the existence of negative eigenvalues for two-dimensional Schr\"odinger operators with real-valued potentials in the weak coupling regime. In his pioneering paper [Simon 1976] from half a cen…
A conjecture of Simon Donaldson is that on a compact $4$-manifold $X^4$ one can flow from a hypersymplectic structure to a hyperk\"ahler structure while remaining in the same cohomology class. To this…
Scalability of evolutionary algorithms refers to assessing how their performance changes as problem size increases. In the area of multi-objective optimisation, research on the scalability of multi-ob…
We develop a general framework to calculate the many-body density of states (DOS) of isolated and interacting quantum systems. Based on the generalized coherent state formalism and the Simon-Lieb boun…
We investigate the impossibility of universally winning trading strategies -- those generating strict profit across all market trajectories -- through three distinct mathematical paradigms. Fundamenta…
We consider a nonlinear constrained heat flow evolving on the manifold $\mathcal{M}=\{v\in L^{2}:\|v\|_{L^{2}}=1\}$ over bounded smooth domains. It is known that the solution corresponding to any nonn…
Measurement of $N_{\rm eff}$ in the CMB (Cosmic Microwave Background) observations, like Planck 2018 and BBN (Big Bang Nucleosynthesis) has already set stringent constraints on the interaction strengt…
We prove that for a residual (and hence dense) subset $\mathcal{G}$ of Riemannian metrics on $S^{n+1}$ in the $C^{3}$ topology, no area-minimizing integral $n$-current that is a boundary admits a sing…
Electro-optic (E/O) modulators are crucial for optical communication but face a trade-off between modulation bandwidth and efficiency. A small footprint could reduce the capacitance and increase the b…
W. L. Ferrar seems to have been the first mathematician to clearly draw a connection between the functional aspects of a summation formula and the behavior of the Dirichlet series underlying it. Takin…
In agricultural robotics, effective observation and localization of fruits present challenges due to occlusions caused by other parts of the tree, such as branches and leaves. These occlusions can res…
This thesis develops a decision-theoretic framework for extracting thermodynamic work from temporal correlations in quantum systems. We model a classical agent -- lacking quantum memory -- performing …
Sabotage games are played on a dynamic graph, in which one agent, called a runner, attempts to reach a goal state, while being obstructed by a demon who at each round removes an edge from the graph. S…
In the context of finite Abelian groups two problems are presented and solved using quantum computing techniques. The first is the well--known Hidden Subgroup Problem, originally solved by Simon in a …
We present a concise dynamical picture of infant-driven household chaos. The framework has three postulations: recurrent daily chaos, overall entropy growth in household organization, and transient lo…
A common paradigm in phase-field models with singular potentials is that global-in-time weak solutions converge to a single equilibrium only after undergoing asymptotic regularization. However, in arX…
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