CytoSet: Predicting clinical outcomes via set-modeling of cytometry data

Single-cell flow and mass cytometry technologies are being increasingly applied in clinical settings, as they enable the simultaneous measurement of multiple proteins across millions of cells within a multi-patient cohort. In this work, we introduce CytoSet, a deep learning model that can directly predict a patient’s clinical outcome from a collection of cells obtained through a blood or tissue sample. Unlike previous work, CytoSet explicitly models the cells profiled in each patient sample as a set, allowing for the use of recently developed permutation invariant architectures. We show that CytoSet achieves state-of-the-art classification performance across a variety of flow and mass cytometry benchmark datasets. Specifically, CytoSet greatly outperforms two baseline models by 20.6% on a large multi-sample clinical flow cytometry dataset. The strong classification performance is further complemented by demonstrated robustness to the number of sub-sampled cells per patient, enabling CytoSet to scale to hundreds of patient samples. Furthermore, we also conducted an ablation study with networks of varying depths to demonstrate that much of the representation power of CytoSet comes from the permutation-equivalent architectures. The superior performance achieved by the set-based architectures used in CytoSet suggests that clinical cytometry data can be appropriately interpreted and studied as sets. The code is publicly available at https://github.com/CompCy-lab/cytoset.

A class of constacyclic codes over the ring Z4[u,v]/ and their Gray images

In this paper, we study (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes over the ring Z4 + uZ4 + vZ4 + uvZ4 where u2 = v2 = 0,uv = vu. We define some new Gray maps and show that the Gray images of (1 + 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Further, we determine the structure of (1 + 2u + 2v)-constacyclic codes of odd length n.

A study of constacyclic codes over the ring ℤ4[u]/〈u2 − 3〉

In this paper, we study [Formula: see text]-constacyclic codes over the ring [Formula: see text], where [Formula: see text] for [Formula: see text] and [Formula: see text], respectively. We define some new Gray maps from [Formula: see text] to the copies of [Formula: see text]. It is shown that Gray images of [Formula: see text]-constacyclic codes over [Formula: see text] are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over [Formula: see text]. Further, we extend and obtain cyclic codes, [Formula: see text]-constacyclic codes and permutation equivalent to quasi-cyclic codes over [Formula: see text], respectively, as Gray images of skew [Formula: see text]-constacyclic codes over [Formula: see text].

Analysis of permutation equivalence in -adhesive transformation systems with negative application conditions

$\mathcal{M}$-adhesive categories provide an abstract framework for a large variety of specification frameworks for modelling distributed and concurrent systems. They extend the well-known frameworks of adhesive and weak adhesive HLR categories and integrate high-level constructs such as attribution as in the case of typed attributed graphs.In the current paper, we investigate$\mathcal{M}$-adhesive transformation systems including negative application conditions (NACs) for transformation rules, which are often used in applications. For such systems, we propose an original equivalence on transformation sequences, calledpermutation equivalence, that is coarser than the classical switch equivalence. We also present a general construction of deterministic processes for$\mathcal{M}$-adhesive transformation systems based on subobject transformation systems. As a main result, we show that the process obtained from a transformation sequence identifies its equivalence class of permutation-equivalent transformation sequences. Moreover, we show how the analysis of this process can be reduced to the analysis of the reachability graph of a generated Place/Transition Petri net. This net encodes the dependencies between rule applications of the transformation sequence, including the inhibiting effects of the NACs.

More on optimal allocation of components in coherent systems

More applications of the principle for interchanging components due to Boland et al. (1989) in reliability theory are presented. In the context of active redundancy improvement we show that if two nodes are permutation equivalent then allocating a redundancy component to the weaker position always results in a larger increase in system reliability, which generalizes a previous result due to Boland et al. (1992). In the case of standby redundancy enhancement, we prove that a series (parallel) system is the only system for which standby redundancy at the component level is always more (less) effective than at the system level. Finally, the principle for interchanging components is extended from binary systems to the more complicated multistate systems.

More on optimal allocation of components in coherent systems

More applications of the principle for interchanging components due to Boland et al. (1989) in reliability theory are presented. In the context of active redundancy improvement we show that if two nodes are permutation equivalent then allocating a redundancy component to the weaker position always results in a larger increase in system reliability, which generalizes a previous result due to Boland et al. (1992). In the case of standby redundancy enhancement, we prove that a series (parallel) system is the only system for which standby redundancy at the component level is always more (less) effective than at the system level. Finally, the principle for interchanging components is extended from binary systems to the more complicated multistate systems.