Related papers: Simple trace criterion for classification of multi…
A variant of the trace in a monoidal category is given in the setting of closed monoidal derivators, which is applicable to endomorphisms of fiberwise dualizable objects. Functoriality of this trace is established. As an application, an…
Molecules have a number of distinct properties whose importance and application vary. Often, in reality, labels for some properties are hard to achieve despite their practical importance. A common solution to such data scarcity is to use…
The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multi-layer networks, i.e. networks where each layer stands for…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
A classification is given for factorizations of almost simple groups with at least one factor solvable, and it is then applied to characterize $s$-arc-transitive Cayley graphs of solvable groups, leading to a striking corollary: Except the…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
The transition from monolayers to multilayered structures in bacterial colonies is a fundamental step in biofilm development. Observed across different morphotypes and species, this transition is triggered within freely growing bacterial…
Causal discovery, the task of automatically constructing a causal model from data, is of major significance across the sciences. Evaluating the performance of causal discovery algorithms should ideally involve comparing the inferred models…
Single-cell reference atlases are large-scale, cell-level maps that capture cellular heterogeneity within an organ using single cell genomics. Given their size and cellular diversity, these atlases serve as high-quality training data for…
Multiclass prediction is the problem of classifying an object into a relevant target class. We consider the problem of learning a multiclass predictor that uses only few features, and in particular, the number of used features should…
The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…
If a matrix $A$ has rank $r$, then its row echelon form (from elimination) contains the identity matrix in its first $r$ independent columns. How do we \emph{interpret the matrix} $F$ that appears in the remaining columns of that echelon…
Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several…
Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for…
The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
We establish Multilayer Correlation Clustering, a novel generalization of Correlation Clustering to the multilayer setting. In this model, we are given a series of inputs of Correlation Clustering (called layers) over the common set $V$ of…
Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…
The study of complex networks that account for different types of interactions has become a subject of interest in the last few years, specially because its representational power in the description of users interactions in diverse online…
In conventional formulations of multilayer feedforward neural networks, the individual layers are customarily defined by explicit functions. In this paper we demonstrate that defining individual layers in a neural network \emph{implicitly}…