This paper introduces a novel finite Zak transform (FZT)-aided framework for constructing multiple zero-correlation zone (ZCZ) sequence sets with optimal correlation properties. Specifically, each sequence is perfect with zero auto-correlation sidelobes, each ZCZ sequence set meets the Tang-Fan-Matsufuji bound with equality, and the maximum inter-set cross-correlation of multiple sequence sets meets the Sarwate bound with equality. Our study shows that these sequences can be sparsely expressed in the Zak domain through properly selected index and phase matrices. Particularly, it is found that the maximum inter-set cross-correlation beats the Sarwate bound if every index matrix is a circular Florentine array. Several construction methods of multiple ZCZ sequence sets are proposed, demonstrating both the optimality and high flexibility. Additionally, it is shown that excellent synchronization performance can be achieved by the proposed sequences in orthogonal-time-frequency-space (OTFS) systems.

Spectrally-null-constrained (SNC) sequences, characterized by a good zero correlation zone (ZCZ) property, are applied in contemporary communication and radar systems that operate across a non-continuous spectrum. Although a large number of previous studies have been conducted, there has been no work on constructing optimal SNC sequence sets with all-zero inter-set cross-correlation (AZISCC). In this letter, we present a method for constructing SNC-ZCZ sequence sets utilizing the finite Zak transform (FZT). The obtained multiple SNC-ZCZ sequence sets are optimal, and they achieve the theoretical bound. The cross-correlation between sequence sets is 0, and the inter-cell interference can be eliminated. Furthermore, the sparse representation of the sequences is convenient for performing signal processing tasks in many radar, sonar, and communication applications.

Phase separation is an important mechanism that mediates the spatial distribution of proteins in different cellular compartments. While phase-separated proteins share certain sequence characteristics, including intrinsically disordered regions (IDRs) and prion-like domains, such characteristics are insufficient for making accurate predictions; thus, a proteome-wide understanding of phase separation is currently lacking. Here, we define phase-separated proteomes based on the systematic analysis of immunofluorescence images of 12 073 proteins in the Human Protein Atlas. The analysis of these proteins reveals that phase-separated candidate proteins exhibit higher IDR contents, higher mean net charge and lower hydropathy and prefer to bind to RNA. Kinases and transcription factors are also enriched among these candidate proteins. Strikingly, both phase-separated kinases and phase-separated transcription factors display significantly reduced substrate specificity. Our work provides the first global view of the phase-separated proteome and suggests that the spatial proximity resulting from phase separation reduces the requirement for motif specificity and expands the repertoire of substrates. The source code and data are available at https://github.com/cheneyyu/deepphase.