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A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. An explicit lower bound…
Low-bit forward evaluation is an attractive route to memory-efficient zeroth-order (ZO) adaptation: the optimizer needs only scalar losses, and the model can be queried near deployment precision. The obstacle is that a quantized ZO query is…
In this letter, we propose a novel approach to concurrently measure the complementary $CP$ violation observables induced by $T$-odd correlations and their corresponding $T$-even counterparts, where $T$ represents time reversal. Our analysis…
We consider a system of harmonic oscillators with short range interactions and we study their correlation functions when the initial data is sampled with respect to the Gibbs measure. Such correlation functions display rapid oscillations…
The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers [RW08, ORW08]. In this paper we study the correlation structure among different functionals such as nodal…
We describe some recent work concerning Gorenstein liaison of codimension two subschemes of a projective variety. Applications make use of the algebraic theory of maximal Cohen-Macaulay modules, which we review in an Appendix.
Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side-channel and fault injection…
Sliding cable system with frictions is encountered in many engineering applications. Such system is typically characterized by existences of complex and varied motion states of different sliding nodes (pulleys), which leads to significant…
The "maximum similarity correlation" definition introduced in this study is motivated by the seminal work of Szekely et al on "distance covariance" (Ann. Statist. 2007, 35: 2769-2794; Ann. Appl. Stat. 2009, 3: 1236-1265). Instead of using…
To construct a Paley graph, we fix a finite field and consider its elements as vertices of the Paley graph. Two vertices are connected by an edge if their difference is a square in the field. We will study some important properties of the…
Very recently, we have introduced correlation consistent effective core potentials (ccECPs) derived from many-body approaches with the main target being its use in explicitly correlated methods but also in mainstream approaches. The ccECPs…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
The focus of this thesis is the study and construction of covering arrays, relying on maximal period sequences and other tools from finite fields. A covering array of strength $t$, denoted $\mathrm{CA}(N; t, k,v)$, is an $N\times k$ array…
We say that a sequence $(x_n)_{n \in \mathbb{N}}$ in $[0,1)$ has Poissonian pair correlations if \begin{equation*} \lim_{N \to \infty} \frac{1}{N} \# \left \lbrace 1 \leq l \neq m \leq N: \| x_l - x_m \| \leq \frac{s}{N} \right \rbrace = 2s…
Cosmological correlators are fundamental observables in an expanding universe and are highly non-trivial functions even at tree-level. In this work, we uncover novel structures in the space of such tree-level correlators that enable us to…
We consider the rare decay channels of the $Z$ boson: $Z \to \text{two}\ \textrm{jets} + \gamma$ and $Z \to \text{two}\ \textrm{jets} +2\, \gamma$. To obtain the widths and distributions for these processes, we compute the effect of NLO QCD…
Real-world graphs generally have only one kind of tendency in their connections. These connections are either homophily-prone or heterophily-prone. While graphs with homophily-prone edges tend to connect nodes with the same class (i.e.,…
We discuss the odd-frequency pairing correlations discovered by Zachar, Kivelson and Emery (ZKE) in a one dimensional Kondo lattice. A lattice model that realizes the continuum theory of ZKE is introduced and the correlations it gives rise…
We study states of one- and two-dimensional spin systems that are constructed as correlators within the conformal field theory of a massless, free boson. In one dimension, these are good variational wave functions for XXZ spin chains and…
We examine the contributions of various couplings in general ZZH and gammaZH interactions arising from new physics to the Higgs production process e+e- --> HZ, followed by the decay of the Z into a charged-lepton pair. We take into account…