Convergence of algorithms for reconstructing convex bodies and directional measures

We investigate algorithms for reconstructing a convex body $K$ in $\mathbb {R}^n$ from noisy measurements of its support function or its brightness function in $k$ directions $u_1,...,u_k$. The key idea of these algorithms is to construct a convex polytope $P_k$ whose support function (or brightness function) best approximates the given measurements in the directions $u_1,...,u_k$ (in the least squares sense). The measurement errors are assumed to be stochastically independent and Gaussian. It is shown that this procedure is (strongly) consistent, meaning that, almost surely, $P_k$ tends to $K$ in the Hausdorff metric as $k\to\infty$. Here some mild assumptions on the sequence $(u_i)$ of directions are needed. Using results from the theory of empirical processes, estimates of rates of convergence are derived, which are first obtained in the $L_2$ metric and then transferred to the Hausdorff metric. Along the way, a new estimate is obtained for the metric entropy of the class of origin-symmetric zonoids contained in the unit ball. Similar results are obtained for the convergence of an algorithm that reconstructs an approximating measure to the directional measure of a stationary fiber process from noisy measurements of its rose of intersections in $k$ directions $u_1,...,u_k$. Here the Dudley and Prohorov metrics are used. The methods are linked to those employed for the support and brightness function algorithms via the fact that the rose of intersections is the support function of a projection body.Comment: Published at http://dx.doi.org/10.1214/009053606000000335 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Content of Polynomials Over Semirings and Its Applications

In this paper, we prove that Dedekind-Mertens lemma holds only for those semimodules whose subsemimodules are subtractive. We introduce Gaussian semirings and prove that bounded distributive lattices are Gaussian semirings. Then we introduce weak Gaussian semirings and prove that a semiring is weak Gaussian if and only if each prime ideal of this semiring is subtractive. We also define content semialgebras as a generalization of polynomial semirings and content algebras and show that in content extensions for semirings, minimal primes extend to minimal primes and discuss zero-divisors of a content semialgebra over a semiring who has Property (A) or whose set of zero-divisors is a finite union of prime ideals. We also discuss formal power series semirings and show that under suitable conditions, they are good examples of weak content semialgebras.Comment: Final version published at J. Algebra Appl., one reference added, three minor editorial change

Large eddy simulations and direct numerical simulations of high speed turbulent reacting flows

This research is involved with the implementations of advanced computational schemes based on large eddy simulations (LES) and direct numerical simulations (DNS) to study the phenomenon of mixing and its coupling with chemical reactions in compressible turbulent flows. In the efforts related to LES, a research program was initiated to extend the present capabilities of this method for the treatment of chemically reacting flows, whereas in the DNS efforts, focus was on detailed investigations of the effects of compressibility, heat release, and nonequilibrium kinetics modeling in high speed reacting flows. The efforts to date were primarily focussed on simulations of simple flows, namely, homogeneous compressible flows and temporally developing hign speed mixing layers. A summary of the accomplishments is provided

A note on the Schur multiplier of a nilpotent Lie algebra

For a nilpotent Lie algebra $L$ of dimension $n$ and dim$(L^2)=m$, we find the upper bound dim$(M(L))\leq {1/2}(n+m-2)(n-m-1)+1$, where $M(L)$ denotes the Schur multiplier of $L$. In case $m=1$ the equality holds if and only if $L\cong H(1)\oplus A$, where $A$ is an abelian Lie algebra of dimension $n-3$ and H(1) is the Heisenberg algebra of dimension 3.Comment: Paper in press in Comm. Algebra with small revision

Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) for the computational analyses of high speed reacting flows

The principal objective is to extend the boundaries within which large eddy simulations (LES) and direct numerical simulations (DNS) can be applied in computational analyses of high speed reacting flows. A summary of work accomplished during the last six months is presented

Electrical stimulation of the ear, head, cranial nerve, or cortex for the treatment of tinnitus: a scoping review

Tinnitus is defined as the perception of sound in the absence of an external source. It is often associated with hearing loss and is thought to result from abnormal neural activity at some point or points in the auditory pathway, which is incorrectly interpreted by the brain as an actual sound. Neurostimulation therapies therefore, which interfere on some level with that abnormal activity, are a logical approach to treatment. For tinnitus, where the pathological neuronal activity might be associated with auditory and other areas of the brain, interventions using electromagnetic, electrical, or acoustic stimuli separately, or paired electrical and acoustic stimuli, have been proposed as treatments. Neurostimulation therapies should modulate neural activity to deliver a permanent reduction in tinnitus percept by driving the neuroplastic changes necessary to interrupt abnormal levels of oscillatory cortical activity and restore typical levels of activity. This change in activity should alter or interrupt the tinnitus percept (reduction or extinction) making it less bothersome. Here we review developments in therapies involving electrical stimulation of the ear, head, cranial nerve, or cortex in the treatment of tinnitus which demonstrably, or are hypothesised to, interrupt pathological neuronal activity in the cortex associated with tinnitus

A review on impedimetric immunosensors for pathogen and biomarker detection

Since the discovery of antibiotics in the first quarter of the twentieth century, their use has been the principal approach to treat bacterial infection. Modernized medicine such as cancer therapy, organ transplantation or advanced major surgeries require effective antibiotics to manage bacterial infections. However, the irresponsible use of antibiotics along with the lack of development has led to the emergence of antimicrobial resistance which is considered a serious global threat due to the rise of multidrug-resistant bacteria (Wang et al. in Antibiotic resistance: a rundown of a global crisis, pp. 1645–1658, 2018). Currently employed diagnostics techniques are microscopy, colony counting, ELISA, PCR, RT-PCR, surface-enhanced Raman scattering and others. These techniques provide satisfactory selectivity and sensitivity (Joung et al. in Sens Actuators B Chem 161:824–831, 2012). Nevertheless, they demand specialized personnel and expensive and sophisticated machinery which can be labour-intensive and time-consuming, (Malvano et al. in Sensors (Switzerland) 18:1–11, 2018; Mantzila et al. in Anal Chem 80:1169–1175, 2008). To get around these problems, new technologies such as biosensing and lab-on-a-chip devices have emerged in the last two decades. Impedimetric immunosensors function by applying electrochemical impedance spectroscopy to a biosensor platform using antibodies or other affinity proteins such as Affimers (Tiede et al. in Elife 6(c):1–35, 2017) or other binding proteins (Weiss et al. in Electrochim Acta 50:4248–4256, 2005) as bioreceptors, which provide excellent sensitivity and selectivity. Pre-enrichment steps are not required and this allows miniaturization and low-cost. In this review different types of impedimetric immunosensors are reported according to the type of electrode and their base layer materials, either self-assembled monolayers or polymeric layers, composition and functionalization for different types of bacteria, viruses, fungi and disease biomarkers. Additionally, novel protein scaffolds, both antibody derived and non-antibody derived, used to specifically target the analyte are considered