Fluorescence tomographic imaging in turbid media using early-arriving photons and Laplace transforms

We present a multichannel tomographic technique to detect fluorescent objects embedded in thick (6.4 cm) tissue-like turbid media using early-arriving photons. The experiments use picosecond laser pulses and a streak camera with single photon counting capability to provide short time resolution and high signal-to-noise ratio. The tomographic algorithm is based on the Laplace transform of an analytical diffusion approximation of the photon migration process and provides excellent agreement between the actual positions of the fluorescent objects and the experimental estimates. Submillimeter localization accuracy and 4- to 5-mm resolution are demonstrated. Moreover, objects can be accurately localized when fluorescence background is present. The results show the feasibility of using early-arriving photons to image fluorescent objects embedded in a turbid medium and its potential in clinical applications such as breast tumor detection.

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms

A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.

Laplace Transforms pdf

Exam questions and solutions in PDF

Laplace Transforms

Exam questions and solutions in LaTex

On q-Laplace Transforms of the q-Bessel Functions

Mathematics Subject Classification: 33D15, 44A10, 44A20

Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation?

Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата.

A Flexible Architecture for the Computation of Direct and Inverse Transforms in H.264/AVC Video Codecs

A new high throughput and scalable architecture for unified transform coding in H.264/AVC is proposed in this paper. Such flexible structure is capable of computing all the 4x4 and 2x2 transforms for Ultra High Definition Video (UHDV) applications (4320x7680@ 30fps) in real-time and with low hardware cost. These significantly high performance levels were proven with the implementation of several different configurations of the proposed structure using both FPGA and ASIC 90 nm technologies. In addition, such experimental evaluation also demonstrated the high area efficiency of theproposed architecture, which in terms of Data Throughput per Unit of Area (DTUA) is at least 1.5 times more efficient than its more prominent related designs(1).

Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities

This paper shows that certain quotients of entire functions are characteristic functions. Under some conditions, we provide expressions for the densities of such characteristic functions which turn out to be generalized Dirichlet series which in turn can be expressed as an infinite linear combination of exponential or Laplace densities. We apply these results to several examples.

Hankel and Toeplitz transforms on H 1: continuity, compactness and Fredholm properties

We revisit the boundedness of Hankel and Toeplitz operators acting on the Hardy space H 1 and give a new proof of the old result stating that the Hankel operator H a is bounded if and only if a has bounded logarithmic mean oscillation. We also establish a sufficient and necessary condition for H a to be compact on H 1. The Fredholm properties of Toeplitz operators on H 1 are studied for symbols in a Banach algebra similar to C + H ∞ under mild additional conditions caused by the differences in the boundedness of Toeplitz operators acting on H 1 and H 2.

Estudos de imagens provenientes de membranas de borracha natural com aditivos metálicos utilizando técnicas de Fourier, Gabor e Wavelets

Pós-graduação em Ciência e Tecnologia de Materiais - FC

A note on the hypercomplex riemann-cauchy like relations for quaternions and laplace equations

In this Note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier [1]. As in the theory of functions of a complex variable, it is expected that this new set of Laplace-Like equations might be applied to a large number of Physical problems, providing new insights in the Classical Fields Theory.

Three-Dimensional Analysis of Spiny Dendrites Using Straightening and Unrolling Transforms

Current understanding of the synaptic organization of the brain depends to a large extent on knowledge about the synaptic inputs to the neurons. Indeed, the dendritic surfaces of pyramidal cells (the most common neuron in the cerebral cortex) are covered by thin protrusions named dendritic spines. These represent the targets of most excitatory synapses in the cerebral cortex and therefore, dendritic spines prove critical in learning, memory and cognition. This paper presents a new method that facilitates the analysis of the 3D structure of spine insertions in dendrites, providing insight on spine distribution patterns. This method is based both on the implementation of straightening and unrolling transformations to move the analysis process to a planar, unfolded arrangement, and on the design of DISPINE, an interactive environment that supports the visual analysis of 3D patterns.

Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99

The Effect of a threshold proportional reinsurance strategy on ruin probabilities

[spa] En un modelo de Poisson compuesto, definimos una estrategia de reaseguro proporcional de umbral : se aplica un nivel de retención k1 siempre que las reservas sean inferiores a un determinado umbral b, y un nivel de retención k2 en caso contrario. Obtenemos la ecuación íntegro-diferencial para la función Gerber-Shiu, definida en Gerber-Shiu -1998- en este modelo, que nos permite obtener las expresiones de la probabilidad de ruina y de la transformada de Laplace del momento de ruina para distintas distribuciones de la cuantía individual de los siniestros. Finalmente presentamos algunos resultados numéricos.