Fractional Hadamard powers of symmetric positive-definite matrices

Let A = (aij) andB = (bij) be matrices of the same size. Then their Hadamard product (also called Schur product) A B is dened by entrywise multiplication: A B = (aij bij) . The Hadamard unit matrix is the matrix U all of whose entries are 1 (the size of U being understood). A matrix A is Hadamard invertible if all its entries are non-zero, and A (= (a ij is then called the Hadamard inverse of A. IfB is Hadamard invertible, then the Hadamard quotient A =B of A and B is (aijb ij The k-fold Hadamard product A k of A with itself (k 0) is called the k-th Hadamard power of A; thus (aij) k = (a k ij ). In particular, A 0 = U (conventionally we set 0 0 = 1). If A is Hadamard invertible, then A k can be dened for negative integers as well, in an obvious manner. For more information on the Hadamard product, see [7, Chapter 5] and [5]

New nonlinear dielectric materials: Linear electrorheological fluids under the influence of electrostriction

The usual approach to the development of new nonlinear dielectric materials focuses on the search for materials in which the components possess an inherently large nonlinear dielectric response. In contrast, based on thermodynamics, we have presented a first-principles approach to obtain the electrostriction-induced effective third-order nonlinear susceptibility for the electrorheological (ER) fluids in which the components have inherent linear, rather than nonlinear, responses. In detail, this kind of nonlinear susceptibility is in general of about the same order of magnitude as the compressibility of the linear ER fluid at constant pressure. Moreover, our approach has been demonstrated in excellent agreement with a different statistical method. Thus, such linear ER fluids can serve as a new nonlinear dielectric material.Comment: 11 page

Propagation of the surface plasmon polaritons through gradient index and periodic structures

We study the propagation of surface electromagnetic waves along the metallic surface covered by various layered dielectric structures. We show that strong radiative losses typical for the scattering of the surface wave can be considerably suppressed when single dielectric step is substituted by gradient index or periodic layered structure

Restoration Of Dual-Frequency Signals With Nonlinear Propagation In Fibers With Positive Group-Velocity Dispersion

It is shown experimentally and theoretically that a sinusoidally modulated pulse evolves with time into a train of dark soliton-like pulses and then returns to its initial sinusoidal shape on propagation through a nonlinear single-mode fiber with positive group velocity dispersion. The experimental results are in agreement with predictions from the nonlinear Schrodinger equation

Smoothed Analysis of Tensor Decompositions

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results. Efficient decomposition in the overcomplete case (where rank exceeds dimension) is particularly challenging. We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension). In this setting, we show that our algorithm is robust to inverse polynomial error -- a crucial property for applications in learning since we are only allowed a polynomial number of samples. While algorithms are known for exact tensor decomposition in some overcomplete settings, our main contribution is in analyzing their stability in the framework of smoothed analysis. Our main technical contribution is to show that tensor products of perturbed vectors are linearly independent in a robust sense (i.e. the associated matrix has singular values that are at least an inverse polynomial). This key result paves the way for applying tensor methods to learning problems in the smoothed setting. In particular, we use it to obtain results for learning multi-view models and mixtures of axis-aligned Gaussians where there are many more "components" than dimensions. The assumption here is that the model is not adversarially chosen, formalized by a perturbation of model parameters. We believe this an appealing way to analyze realistic instances of learning problems, since this framework allows us to overcome many of the usual limitations of using tensor methods.Comment: 32 pages (including appendix

THE DYNAMICS OF ANTIGEN SPECIFIC PROLIFERATIVE RESPONSES OF LYMPHOCYTES AT EARLY STAGES OF BOVINE PARATUBERCULOSIS INFECTION

The present study was aimed to quantify the dynamics of early antigen specific proliferative responses of lymphocytes to (protein) antigens associated with experimentalMycobacterium avium subsp. paratuberculosis (Mp) infection cattle. The data were collected from20 experimentally infected calves, and 10 uninfected control animals, during the first 2 years oftheir lives. Several purified protein derivative antigens (Ppdp, Ppda, and Ppdb), tworecombinant Mp heatshock proteins (Hsp65 and Hsp70) and whole bacteria (sonicated Mpstrain 316F) were used to measure lymphocyte proliferation in a lymphocyte proliferationassay. Data were analyzed using a linear mixed effect (LME) model. The results showedsignificant group and timed effects for all antigens tested. At several time points, the responsesin the infected group were found significantly higher as compared to control group. The Ppdantigens induced similar lymphocyte proliferation patterns, as compared to whole bacteriaantigen and Hsp70. These results indicated that the antigen specific proliferative responses oflymphocytes differs for different antigens, probably related to differences in their availabilityduring different stages of infection. The application of LME model is a useful tool for analyzingthe quantitative longitudinal datasets. Keywords: dynamics, Mp, antigen, LM

Corticospinal beta-band synchronization entails rhythmic gain modulation

Rhythmic synchronization of neurons in the beta or gamma band occurs almost ubiquitously, and this synchronization has been linked to numerous nervous system functions. Many respective studies make the implicit assumption that neuronal synchronization affects neuronal interactions. Indeed, when neurons synchronize, their output spikes reach postsynaptic neurons together, trigger coincidence detection mechanisms, and therefore have an enhanced impact. There is ample experimental evidence demonstrating this consequence of neuronal synchronization, but beyond this, beta/gamma-band synchronization within a group of neurons might also modulate the impact of synaptic input to that synchronized group. This would constitute a separate mechanism through which synchronization affects neuronal interactions, but direct in vivo evidence for this putative mechanism is lacking. Here, we demonstrate that synchronized beta-band activity of a neuronal group modulates the efficacy of synaptic input to that group in-phase with the beta rhythm. This response modulation was not an addition of rhythmic activity onto the average response but a rhythmic modulation of multiplicative input gain. Our results demonstrate that beta-rhythmic activity of a neuronal target group multiplexes input gain along the rhythm cycle. The actual gain of an input then depends on the precision and the phase of its rhythmic synchronization to this target, providing one mechanistic explanation for why synchronization modulates interactions

The Nasal Microbiome in ANCA-Associated Vasculitis:Picking the Nose for Clues on Disease Pathogenesis

PURPOSE OF REVIEW: The onset and progression of small vessel vasculitis associated with anti-neutrophil cytoplasmic antibodies has been linked to microbial infections. Here, we provide a brief overview of the association of nasal colonization of Staphylococcus aureus with ANCA-associated vasculitis (AAV) and discuss several recent studies mapping the nasal microbiome in AAV patients in particular. RECENT FINDINGS: Nasal microbiome studies revealed dysbiosis as a common trait in active AAV which tends to normalize upon immunosuppressive treatment and quiescent disease. However, due to differences in study design, patient selection, and methodology, the reported microbiome profiles differ considerably precluding conclusions on causal relationships. SUMMARY: The microbiome is an emerging area of research in AAV warranting further investigation. Ideally, such studies should be combined with mechanistic studies to unravel key elements related to host-microbe interactions and their relevance for AAV pathogenesis

Robustness of Quadratic Solitons with Periodic Gain

We address the robustness of quadratic solitons with periodic non-conservative perturbations. We find the evolution equations for guiding-center solitons under conditions for second-harmonic generation in the presence of periodic multi-band loss and gain. Under proper conditions, a robust guiding-center soliton formation is revealed.Comment: 5 pages, 5 figures, submitted to Optics Communicatio