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The quantum Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under commutators. This polynomial closure is also typical for 2nd order superintegrable…

For a coherent, binary system made up of binary elements, the exact failure probability requires knowledge of statistical dependence of all orders among the minimal cut sets. Since dependence among the cut sets beyond the second order is…

We prove that the double layer potential operator and the gradient of the single layer potential operator are L_2 bounded for general second order divergence form systems. As compared to earlier results, our proof shows that the bounds for…

The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…

Boolean functions are important primitives in different domains of cryptology, complexity and coding theory. In this paper, we connect the tools from cryptology and complexity theory in the domain of Boolean functions with low polynomial…

It is known that for any class C closed under union and intersection, the Boolean closure of C, the Boolean hierarchy over C, and the symmetric difference hierarchy over C all are equal. We prove that these equalities hold for any…

We consider the sublanguages of Plotkin's PCF obtained by imposing some bound k on the levels of types for which fixed point operators are admitted. We show that these languages form a strict hierarchy, in the sense that a fixed point…

Techniques from Descriptive Set Theory are applied in order to study the Topological Complexity of families of operators naturally connected to ergodic operators in infinite dimensional Banach Spaces. The families of ergodic,…

This work studies the behavior of shallow ReLU networks trained with the logistic loss via gradient descent on binary classification data where the underlying data distribution is general, and the (optimal) Bayes risk is not necessarily…

We present a new method for completing higher derivative corrections for theories that exhibit duality symmetries under reduction. This proposal is based on the observation that duality symmetry in the reduced theory highly constrains the…

We investigate properties of neural networks that use both ReLU and $x^2$ as activation functions and build upon previous results to show that both analytic functions and functions in Sobolev spaces can be approximated by such networks of…

In this paper we extend some previous results on weak pseudo-bosons and on their related bi-coherent states. The role of {\em compatible} functions is discussed in details, and some examples are considered. The pseudo-bosonic ladder…

Set constraints provide a highly general way to formulate program analyses. However, solving arbitrary boolean combinations of set constraints is NEXPTIME-hard. Moreover, while theoretical algorithms to solve arbitrary set constraints…

We consider the problem of finding a two-layer neural network with sigmoid, rectified linear unit (ReLU), or binary step activation functions that "fits" a training data set as accurately as possible as quantified by the training error; and…

Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are…

We introduce a new technique for proving kernelization lower bounds, called cross-composition. A classical problem L cross-composes into a parameterized problem Q if an instance of Q with polynomially bounded parameter value can express the…

We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential…

Understanding the inductive bias of neural networks is critical to explaining their ability to generalise. Here, for one of the simplest neural networks -- a single-layer perceptron with n input neurons, one output neuron, and no threshold…

When working with posets which are not necessarily lattices, one has a lack of lattice operations which causes problems in algebraic constructions. This is the reason why we use the operators Max L and Min U substituting infimum and…

A set is low if A' \le_T HALT. A set is superlow if A' \le_tt HALT. A set is superduperlow if A' \le_btt HALT. While it was known that any superduperlow is decidable it does not seem to be well known. We include two unpublished proofs of…