Concerning the linear dependence of integer translates of exponential box splines

AbstractLet Bξ,λ be the exponential box spline associated with λ ϵ Cn, and an s × n rational matrix with rank s and non-zero columns. Sufficient conditions are provided for the kernel space K(BΞλ)≔a:Zs→C:∑j∈Zsa(j)BΞλ(·− j)=0 to be (i) trivial and (ii) finite dimensional. While these results extend the corresponding theorems known for integer matrices, the methods of proof are discernibly different

Synergistic SNARE modulators of neurotransmission: Complexins and SNAP-29

Neurotransmitter release is a synergistic multistep process occurring at synapses in the brain. Synaptic vesicles containing neurotransmitters tether to the presynaptic active zones, upon which, they are docked and primed to fusion competence by a number of proteins. When an action potential arrives at the terminal, a concomitant rise in the intracellular calcium concentration causes the vesicles to fuse to the presynaptic membrane and release their contents into the synaptic cleft. This process of neuronal excitation-secretion is tightly coupled and mediated by cascades of protein-protein interactions. The native SNAREs Syntaxin-1, SNAP-25 and Synaptobrevin-2 form a core complex that effectively facilitates the vesicle docking-priming-fusion process. Two proteins namely Complexins and SNAP-29 that have been shown to interact with the native SNAREs or their paralogs are detailed in the present study. The SNAP-29 protein belongs to the SNAP-25 family and is believed to be a Golgi-interacting SNARE. It shares only 17% sequence identity with SNAP-25 due to substantial variations in its structure. SNAP-29 was previously shown to interact with multiple Syntaxins localized on various subcellular organelles and was claimed to negatively modulate synaptic transmission in neurons by preventing SNARE disassembly. In the present study, it is proved that conditional loss of SNAP-29 from the forebrain glutamatergic neurons as well as constitutive loss of SNAP-29 in mice did not cause any deficits in transmitter release at glutamatergic or GABAergic synapses. Although constitutive knockout of SNAP-29 in animals caused perinatal lethality, the normal functioning of glutamatergic and GABAergic synapses in the brain could not account for such a dramatic effect. Rather, the lethality seen in these mice was likely due to perturbations in other secretory pathways. The Complexin family comprises of four proteins - Cplx1, Cplx2 are expressed in the brain, while Cplx3 and Cplx4 are prominently expressed in the retina. Previously, it was shown that loss of Cplx1, 2 and 3 in hippocampal neurons (TKO) caused profound deficits in the vesicular release probability and synchronicity of transmitter release. In the present study, this claim was confirmed and also shown that the reintroduction of each of the four wild type Complexins in the TKO via lentiviruses could facilitate synchronous neurotransmission, to variable extents. The strong binding of Cplx1 and Cplx2 to the SNARE complex corroborated their higher efficacy to mediate synchronous transmitter release. In case of Cplx3 and Cplx4, although hardly any binding to the SNARE complex was detectable, they could facilitate transmitter release only if their SNARE binding domain was intact and when targeted to membranes due to their C-terminal CAAX farnesylation. These results prove that all mammalian Complexins are indeed facilitators of synchronous synaptic transmission, and exert their function via SNARE complex binding and additional farnesylation for Cplx3 and Cplx4.

On the sampling and recovery of bandlimited functions via scattered translates of the Gaussian

Let $\lambda$ be a positive number, and let $(x_j:j\in\mathbb Z)\subset\mathbb R$ be a fixed Riesz-basis sequence, namely, $(x_j)$ is strictly increasing, and the set of functions $\{\mathbb R\ni t\mapsto e^{ix_jt}:j\in\mathbb Z\}$ is a Riesz basis ({\it i.e.,} unconditionalbasis) for $L_2[-\pi,\pi]$. Given a function $f\in L_2(\mathbb R)$ whose Fourier transform is zero almost everywhere outside the interval $[-\pi,\pi]$, there is a unique square-summable sequence $(a_j:j\in\mathbb Z)$, depending on $\lambda$ and $f$, such that the function$$I_\lambda(f)(x):=\sum_{j\in\mathbb Z}a_je^{-\lambda(x-x_j)^2}, \qquad x\in\mathbb R,$$ is continuous and square integrable on $(-\infty,\infty)$, and satisfies the interpolatory conditions $I_\lambda (f)(x_j)=f(x_j)$, $j\in\mathbb Z$. It is shown that $I_\lambda(f)$ converges to $f$ in $L_2(\mathbb R)$, and also uniformly on $\mathbb R$, as $\lambda\to0^+$. A multidimensional version of this result is also obtained. In addition, the fundamental functions for the univariate interpolation process are defined, and some of their basic properties, including their exponential decay for large argument, are established. It is further shown that the associated interpolation operators are bounded on $\ell_p(\mathbb Z)$ for every $p\in[1,\infty]$

Modelling electric vehicles use: a survey on the methods

In the literature electric vehicle use is modelled using of a variety of approaches in power systems, energy and environmental analyses as well as in travel demand analysis. This paper provides a systematic review of these diverse approaches using a twofold classification of electric vehicle use representation, based on the time scale and on substantive differences in the modelling techniques. For time of day analysis of demand we identify activity-based modelling (ABM) as the most attractive because it provides a framework amenable for integrated cross-sector analyses, required for the emerging integration of the transport and electricity network. However, we find that the current examples of implementation of AMB simulation tools for EV-grid interaction analyses have substantial limitations. Amongst the most critical there is the lack of realism how charging behaviour is represented

2DOF PID Controller Design for a Class of FOPTD Models–An Analysis with Heuristic Algorithms

AbstractIn recent years, a number of controller design procedures are developed and implemented in process industries to enhance the performance of closed loop processes. In this paper, heuristic algorithm based Two Degrees Of Freedom (2DOF) PID controller design is proposed for a class of First Order Plus Time Delay (FOPTD) systems existing in the literature. Minimization of the weighted sum of multiple objective functions is considered to monitor the heuristic search towards the optimal controller parameters. A detailed comparative analysis between well known heuristic methods, such as Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO), Cuckoo Search (CS) and Firefly Algorithm (FA) are presented. The popular 2DOF PID structures, such as Feed Back Structure (FBS) and Feed Forward Structure (FFS) are considered in this work to enhance the performance of FOPTD systems. From the results, it is noted that, proposed controller provides enhanced results for the reference tracking and disturbance rejection operations

Efficacy of micro algae and cyanobacteria as a live feed for juveniles of shrimp Penaeus monodon

Growth performance and survival of giant tiger shrimp Penaeus monodon fed with five different micro algal diets as a live feed, was evaluated under laboratory condition. The experimental design consisted of feeding the juvenile with micro algal diets and cyanobacterial diets at the same concentrations. Fresh biomass of Chlorella sp., Tetraselmis sp., Isochrysis sp., Synechococcus sp. and Phormidium sp. were used as feed for shrimp P. monodon. Mean total length of shrimp was higher when fed with Chlorella sp. (4.8 cm) followed by Phormidium sp. (4.4 cm) and mean total weight was also higher in shrimp fed with Chlorella sp. (0.59 g) followed by Phormidium sp. (0.569 g). The survival rate of the shrimp was improved in shrimp fed Phormidium sp. (83.33%) and it was decreased in shrimp fed with Isochrysis sp. (36.67%). The shrimp that performed best had significantly more edible flesh (59.35%) (with Chlorella sp.) protein and lipid content (with Phormidium sp.) carbohydrate (with Tetraselmis sp.) Further more, water quality of the tank was better in shrimp fed with Chlorella sp. In general, the research of this study revealed that Chlorella sp. and Phormidium sp. could be used as a live feed for better growth of P. monodon.Key words: Penaeus monodon, micro algae, Synechococcus, Phormidium, Shrimp growth, Chlorella

Vehicle Speed Measurement and Number Plate Detection using Real Time Embedded System

A real time system is proposed to detect moving vehicles that violate the speed limit. A dedicated digital signal processing chip is used to exploit computationally inexpensive image-processing techniques over the video sequence captured from the fixed position video camera for estimating the speed of the moving vehicles. The moving vehicles are detected by analysing the binary image sequences that are constructed from the captured frames by employing the inter-frame difference or the background subtraction techniques. The detected moving vehicles are tracked to estimate their speeds.This project deals with the tracking and following of single object in a sequence of frames and the velocity of the object is determined. The proposed method varies from previous existing methods in tracking moving objects, velocity determination and number plate detection. From the binary image generated, the moving vehicle is tracked using image segmentation of the video frames. The segmentation process is done by using the thresholding and morphological operations on the video frames. The object is visualized and its centroid is calculated. The distance it moved between frame to frame is stored and using this velocity is calculated with the frame rate of video.The images of the speeding vehicles are further analysed to detect license plate image regions. The entire simulation is done in matlab and simulink simulation software. Keywords:morphological;thresholding;segmentation;centroi

Extracting gravity wave parameters during the September 2002 Southern Hemisphere major sudden stratospheric warming using a SANAE imaging riometer

Using absorption data measured by imaging riometer for ionospheric studies (IRIS) located at the South Africa National Antarctic Expedition (SANAE), Antarctica (72° S, 3° W), we extracted the parameters of gravity waves (GW) of periods between 40 and 50 min during late winter/spring of the year 2002, a period of the unprecedented major sudden stratospheric warming (SSW) in the Southern Hemisphere middle atmosphere. During this period, an unprecedented substantial increase of temperature by about 25–30 K throughout the stratosphere was observed. During the period of the occurrence of the major stratospheric warming, there was a reduction of both the GW horizontal phase speeds and the horizontal wavelengths at 90 km. The GW phase speeds and horizontal wavelengths were observed to reach minimum values of about 7 m s⁻¹ and 19 km, respectively, while during the quiet period the average value of the phase speed and horizontal wavelength was approximately 23 m s⁻¹ and 62 km, respectively. The observed event is discussed in terms of momentum flux and also a potential interaction of gravity waves, planetary waves and mean circulation