arXiv research

A 4-dimensional Riemannian manifold equipped with a circulant structure, which is an isometry with respect to the metric and its fourth power is the identity, is considered. The almost product manifold associated with the considered manifold is studied. The relation between the covariant derivatives of the almost produ…

Study on 3D manifolds with circulant structures and their properties.

In this paper, we study deep diagonal circulant neural networks, that is deep neural networks in which weight matrices are the product of diagonal and circulant ones. Besides making a theoretical analysis of their expressivity, we introduced principled techniques for training these models: we devise an initialization s…

It is studied a 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant. On such a manifold a fundamental tensor by the metric and by the covariant derivative of…

Study curvature properties of specific Riemannian manifolds with skew-circulant structures.

A 4-dimensional Riemannian manifold equipped with an additional tensor structure, whose fourth power is the identity, is considered. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant, and it acts as an isometry with respect to the metric. The Riemannian product manifold a…

Study of spheres and circles on a manifold with a specific metric structure.

A new Riemannian manifold with skew-circulant structures and its associated locally conformal Kähler manifold are studied.

We consider a 3-dimensional Riemannian manifold M with two circulant structures -- a metric g and an endomorphism q whose third power is identity. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We obtain some curvature properties of this manifold (M, g, q) and give an e…

We consider a three-dimensional Riemannian manifold equipped with two circulant structures - a metric g and a structure q, which is an isometry with respect to g and the third power of q is minus identity. We discuss some curvature properties of this manifold, we give an example of such a manifold and find a condition …

A 4-dimensional Riemannian manifold equipped with an endomorphism of the tangent bundle, whose fourth power is the identity, is considered. The matrix of this structure in some basis is circulant and the structure acts as an isometry with respect to the metric. Such manifolds are constructed on 4-dimensional real Lie g…

Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To address this problem, we propose Circulant Binary Embedding (CBE) which generates bina…

Paper offers robust recovery for 1-bit sensing with partial Gaussian circulant matrices.

Bitcoin draws the highest degree of attention among cryptocurrencies, while coin mining is one of the most important fashion of profiting in the Bitcoin ecosystem. This paper constructs fresh coin circulation networks by tracking the fresh coin transfer routes with transaction referencing in Bitcoin blockchain. This pa…

We consider a $4$-dimensional Riemannian manifold $M$ equip\-ped with a circulant structure $q$, which is an isometry with respect to the metric $g$ and $q^{4}=\id$, $q^{2}\neq \pm \id$. For such a manifold $(M, g, q)$ we obtain some assertions for the sectional curvatures of $2$-planes. We construct an example of such…

We consider a $3$-dimensional differentiable manifold with two circulant structures -- a Riemannian metric and an additional structure, whose third power is the identity. The structure is compatible with the metric such that an isometry is induced in any tangent space of the manifold. Further, we consider an associated…

We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we construct an infinite series of circulant metrics which are successively almost conform…

C-OPH improves One Permutation Hashing by using a shorter circulant permutation.

In the present paper it is considered a class V of 3-dimensional Riemannian manifolds M with a metric g and two affinor tensors q and S. It is defined another metric \bar{g} in M. The local coordinates of all these tensors are circulant matrices. It is found: 1)\ a relation between curvature tensors R and \bar{R} of g …

We consider a four dimensional Riemannian manifold M with a metric g and an affinor structure q. We note the local coordinates of g and q are circulant matrices. Their first orders are (A, B, C, B), A, B, C \in FM and (0, 1, 0, 0), respectively. Let \nabla be the connection of g. Further, let mu_{1}, mu_{2},mu_{3}, mu_…

We have studied the statistical mechanics of money circulation in a closed economic system. An explicit statistical formulation of the circulation velocity of money is presented for the first time by introducing the concept of holding time of money. The result indicates that the velocity is governed by behavior pattern…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good kernel has to be chosen. Picking a good kernel is a very challenging problem in its…

We consider a class (M, g, q) of four-dimensional Riemannian manifolds M, where besides the metric g there is an additional structure q, whose fourth power is the unit matrix. We use the existence of a local coordinate system such that there the coordinates of g and q are circulant matrices. In this system q has consta…

In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix $A \in \mathbb{R}^{m \times n}$ with $m < n$, by a partial circulant matrix with rows related by circular shifts. Partial circulant matrices admit fast implementations via Fourier tra…

We prove that Pareto theory of circulation of elites results from our wealth evolution model, Kelly criterion for optimal betting and Keynes' observation of "animal spirits" that drive the economy and cause that human financial decisions are prone to excess risk-taking.

This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding literature. The method can be performed in $\mathcal{O}(n\log_2 n)$ operations, where…

The dynamics of an ideal fluid or plasma is constrained by topological invariants such as the circulation of (canonical) momentum or, equivalently, the flux of the vorticity or magnetic fields. In the Hamiltonian formalism, topological invariants restrict the orbits to submanifolds of the phase space. While the coadjoi…

We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals. In the first instance, we deal with the shift-invariant dictionary learning probl…

New model identifies anticyclonic patterns causing drought and heat.

We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount of money held by agents. However, some constraints are needed in generation mecha…

Generalizes Kauffman's clock theorem to surfaces.

Novel Bayesian framework for spatio-temporal neuroimaging data.

This paper circulated previously in a draft version. Now, upon general request, it is about time to distribute the more detailed (and much longer) version. The main technical issues revolve around the fine structure of the compactification of the moduli spaces of flow lines and the obstruction bundle technique, with re…

We introduce a framework and early results for massively scalable Gaussian processes (MSGP), significantly extending the KISS-GP approach of Wilson and Nickisch (2015). The MSGP framework enables the use of Gaussian processes (GPs) on billions of datapoints, without requiring distributed inference, or severe assumption…

New algorithms for efficient learning with long-term rewards in contextual bandits.

The paper uncovers symmetries in large language models through layer-peeled optimization.

We investigate nodal sets of magnetic Schroedinger operators with zero magnetic field, acting on a non simply connected domain in $\r^2$. For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a charactisation of the nodal set, and use this to obtain bounds on the mul…

A graph theory approach defines curl and decomposes vector fields.

Deep learning improves probabilistic river discharge forecasting for hydroelectric power.

Recurrent Neural Networks (RNNs) are becoming increasingly important for time series-related applications which require efficient and real-time implementations. The recent pruning based work ESE suffers from degradation of performance/energy efficiency due to the irregular network structure after pruning. We propose bl…

Recursive Feature Machines show grokking in modular arithmetic without neural networks.

Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense but are assumed to have a low-rank structure when matricized appropriately. Such a…

We propose unitary group convolutions (UGConvs), a building block for CNNs which compose a group convolution with unitary transforms in feature space to learn a richer set of representations than group convolution alone. UGConvs generalize two disparate ideas in CNN architecture, channel shuffling (i.e. ShuffleNet) and…

C-MinHash reduces the number of permutations needed for MinHash from thousands to just two.

We propose a scheme for recycling Gaussian random vectors into structured matrices to approximate various kernel functions in sublinear time via random embeddings. Our framework includes the Fastfood construction as a special case, but also extends to Circulant, Toeplitz and Hankel matrices, and the broader family of s…

We consider a four dimensional Riemannian manifold M with a metric g and an affinor structure q. We note the local coordinates of g and q are circulant matrices. Their first orders are (A, B, C, B)(A, B, C are smooth functions on M) and (0, 1, 0, 0), respectively. Let nabla be the connection of g. Then we obtain: 1) q^…

We study a game-theoretic variant of the maximum circulation problem. In a flow allocation game, we are given a directed flow network. Each node is a rational agent and can strategically allocate any incoming flow to the outgoing edges. Given the strategy choices of all agents, a maximal circulation that adheres to the…

Parastatistic distribution of a total debt owed to a large number of creditors considered in relation to the duration of these debts. The process of debt calculation depends on the fractal dimension of economic system in which this process takes place. Two actual variants of these dimensions are investigated. Critical …