arXiv research

CNN model for efficient wireless spectrum sensing and signal identification.

Kernel method is a very powerful tool in machine learning. The trick of kernel has been effectively and extensively applied in many areas of machine learning, such as support vector machine (SVM) and kernel principal component analysis (kernel PCA). Kernel trick is to define a kernel function which relies on the inner-…

Paper bounds the lowest spectrum of manifolds with curvature constraints.

Spectrum sensing is of critical importance in any cognitive radio system. When the primary user's signal has uncertain parameters, the likelihood ratio test, which is the theoretically optimal detector, generally has no closed-form expression. As a result, spectrum sensing under parameter uncertainty remains an open qu…

A novel approach of training data augmentation and domain adaptation is presented to support machine learning applications for cognitive radio. Machine learning provides effective tools to automate cognitive radio functionalities by reliably extracting and learning intrinsic spectrum dynamics. However, there are two im…

Dynamic spectrum access (DSA) is regarded as an effective and efficient technology to share radio spectrum among different networks. As a secondary user (SU), a DSA device will face two critical problems: avoiding causing harmful interference to primary users (PUs), and conducting effective interference coordination wi…

In all dimensions, we prove that the marked length spectrum of a Riemannian manifold $(M,g)$ with Anosov geodesic flow and non-positive curvature locally determines the metric in the sense that two close enough metrics with the same marked length spectrum are isometric. In addition, we provide a completely new stabilit…

We construct spectral triples in a sense of noncommutative differential geometry, associated with a Riemannian foliation on a compact manifold, and describe its dimension spectrum.

Multi-parameter cognition in a cognitive radio network (CRN) provides a more thorough understanding of the radio environments, and could potentially lead to far more intelligent and efficient spectrum usage for a secondary user. In this paper, we investigate the multi-parameter cognition problem for a CRN where the pri…

Quantum cellular automata form a homology theory.

Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that the second fundamental form vanishes at infinity, and that the surface is not tot…

Study shows a modified cobordism category's first derivative is equivalent to a Thom spectrum.

Let $M^n$ be a closed, connected $n$-manifold. Let $\mtm$ denote the Thom spectrum of its stable normal bundle. A well known theorem of Atiyah states that $\mtm$ is homotopy equivalent to the Spanier-Whitehead dual of $M$ with a disjoint basepoint, $M_+$. This dual can be viewed as the function spectrum, $F(M, S)$, whe…

In this paper, we investigate cost-aware joint learning and optimization for multi-channel opportunistic spectrum access in a cognitive radio system. We investigate a discrete time model where the time axis is partitioned into frames. Each frame consists of a sensing phase, followed by a transmission phase. During the …

MFSSA improves reconstruction accuracy of multivariate functional time series.

Different neural network (NN) architectures have different advantages. Convolutional neural networks (CNNs) achieved enormous success in computer vision, while recurrent neural networks (RNNs) gained popularity in speech recognition. It is not known which type of NN architecture is the best fit for classification of co…

Essential spectrum of differential forms on curved manifolds is connected.

Opportunistic spectrum access is one of the emerging techniques for maximizing throughput in congested bands and is enabled by predicting idle slots in spectrum. We propose a kernel-based reinforcement learning approach coupled with a novel budget-constrained sparsification technique that efficiently captures the envir…

Motivated by the theory of quantum waveguides, we investigate the spectrum of the Laplacian, subject to Dirichlet boundary conditions, in a curved strip of constant width that is defined as a tubular neighbourhood of an infinite curve in a two-dimensional Riemannian manifold. Under the assumption that the strip is asym…

This paper studies the problem of spectrum shortage in an unmanned aerial vehicle (UAV) network during critical missions such as wildfire monitoring, search and rescue, and disaster monitoring. Such applications involve a high demand for high-throughput data transmissions such as real-time video-, image-, and voice- st…

Study compares spectral properties of a specific tensor in geometry.

Corners can be identified by a drum's sound spectrum.

Given a principal bundle over a closed manifold, G --> P --> M, let P^{Ad} --> M be the associated adjoint bundle. Gruher and Salvatore showed that the Thom spectrum (P^{Ad})^{-TM} is a ring spectrum whose corresponding product in homology is a Chas-Sullivan type string topology product. We refer to this spectrum as th…

In this paper, we address the general case of a coordinated secondary network willing to exploit communication opportunities left vacant by a licensed primary network. Since secondary users (SU) usually have no prior knowledge on the environment, they need to learn the availability of each channel through sensing techn…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods…

The paper solves the Steklov spectral inverse problem for conformal metrics.

Muon replaces matrix gradient with polar factor, optimizing flat spectrum updates

We show that the Chas-Sullivan loop product, a combination of the Pontrjagin product on the fiber and intersection product on the base, makes sense on the total space homology of any fiberwise monoid E over a closed oriented manifold M. More generally the Thom spectrum E^{-TM} is a ring spectrum. Similarly a fiberwise …

Let $M^m$ be a minimal properly immersed submanifold in an ambient space close, in a suitable sense, to the space form $\mathbb{N}^n_k$ of curvature $-k\le 0$. In this paper, we are interested in the relation between the density function $Θ(r)$ of $M^m$ and the spectrum of the Laplace-Beltrami operator. In particular, …

Study of bound states in quantum layers with confining potentials.

Owing to the ever-increasing demand in wireless spectrum, Cognitive Radio (CR) was introduced as a technique to attain high spectral efficiency. As the number of secondary users (SUs) connecting to the cognitive radio network is on the rise, there is an imminent need for centralized algorithms that provide high through…

We give a basic treatment of lattices $Γ$ in these groups. Certain tori $T_F$ and $T_B$ provide the model fiber and the base for a submersion of $Γ\backslash N$. This submersion may not be pseudoriemannian in the usual sense, because the tori may be degenerate. We then begin the study of periodic geodesics in these com…

This letter presents the sparse vector signal detection from one bit compressed sensing measurements, in contrast to the previous works which deal with scalar signal detection. In this letter, available results are extended to the vector case and the GLRT detector and the optimal quantizer design are obtained. Also, a …

A certain spectrum, indexed by a\in[0,\infty], of upper bounds P_a(X;x) on the tail probability P(X\geq x), with P_0(X;x)=P(X\geq x) and P_\infty(X;x) being the best possible exponential upper bound on P(X\geq x), is shown to be stable and monotonic in a, x, and X, where x is a real number and X is a random variable. T…

Cappell and Shaneson pointed out in 1978 interesting properties of Browder - Livesay invariants which are similar to differentials in some spectral sequence. Such spectral sequence was constructed in 1991 by Hambleton and Kharshiladze. This spectral sequence is closely related to a problem of realization of elements of…

Deformation K-theory associates to each discrete group G a spectrum built from spaces of finite dimensional unitary representations of G. In all known examples, this spectrum is 2-periodic above the rational cohomological dimension of G (minus 2), in the sense that T. Lawson's Bott map is an isomorphism on homotopy in …

A new debiasing method for high-dimensional regression with applications to PCR.

In this work, we first describe a framework for the application of Reinforcement Learning (RL) control to a radar system that operates in a congested spectral setting. We then compare the utility of several RL algorithms through a discussion of experiments performed on Commercial off-the-shelf (COTS) hardware. Each RL …

We generalize the Novikov inequalities for 1-forms in two different directions: first, we allow non-isolated critical points (assuming that they are non-degenerate in the sense of R.Bott), and, secondly, we strengthen the inequalities by means of twisting by an arbitrary flat bundle. We also obtain an $L^2$ version of …

For a Riemannian closed spin manifold and under some topological assumption (non-zero $\hat{A}$-genus or enlargeability in the sense of Gromov-Lawson), we give an optimal upper bound for the infimum of the scalar curvature in terms of the first eigenvalue of the Laplacian. The main difficulty lies in the study of the o…

We generalize the Novikov inequalities for 1-forms in two different directions: first, we allow non-isolated critical points (assuming that they are non-degenerate in the sense of R.Bott), and, secondly, we strengthen the inequalities by means of twisting by an arbitrary flat bundle. The proof uses Bismut's modificatio…

Unsupervised dimension selection is an important problem that seeks to reduce dimensionality of data, while preserving the most useful characteristics. While dimensionality reduction is commonly utilized to construct low-dimensional embeddings, they produce feature spaces that are hard to interpret. Further, in applica…

We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between…

Generic density of equivariant min-max hypersurfaces in Riemannian manifolds.

Adversarial examples in machine learning for images are widely publicized and explored. Illustrations of misclassifications caused by slightly perturbed inputs are abundant and commonly known (e.g., a picture of panda imperceptibly perturbed to fool the classifier into incorrectly labeling it as a gibbon). Similar atta…

For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a closed manifold $M^{n+1}$, $3\leq (n+1)\leq 7$, we prove that there is a sequence of closed, smooth, embedded, connected minimal hypersurfaces that is equidistributed in $M$. This gives a quantitative version of the main result of \cite{irie-marques…

We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in terms of modules over a stack of parametrized spectra and in terms of diagrams o…

We define a new spectrum for compact length spaces and Riemannian manifolds called the "covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers $δ>0$ which identify the distinct $δ$ covers of the space. We investigat…