Ramón J. Aliaga

Universitat Politècnica de València | UPV ·  Institute for Pure and Applied Mathematics (IUMPA)

A scheme is proposed for hardware estimation of the location of zero crossings of sampled signals with sub-sample resolution for timing applications, that consists in interpolating the signal with a cubic spline near the zero crossing and then finding the root of the resulting polynomial. An iterative algorithm based on the bisection method is pres...

We analyze the relationship between Borel measures and continuous linear functionals on the space $\textrm{Lip}_0(M)$ of Lipschitz functions on a complete metric space $M$. In particular, we describe continuous functionals arising from measures and vice versa. In the case of weak$^\ast $ continuous functionals, that is, members of the Lipschitz-fre...

We prove that all extreme points of the unit ball of a Lipschitz-free space over a compact metric space have finite support. Combined with previous results, this completely characterizes extreme points and implies that all of them are also extreme points in the bidual ball. For the proof, we develop some properties of an integral representation of...

We prove that Pelczynski's property (V*) is locally determined for Lipschitz-free spaces, and obtain several sufficient conditions for it to hold. We deduce that $\mathcal{F}(M)$ has property (V*) when the complete metric space $M$ is locally compact and purely 1-unrectifiable, a Hilbert space, or belongs to a class of Carnot-Carathéodory spaces sa...

We show that the Lipschitz‐free space with the Radon–Nikodým property and a Daugavet point recently constructed by Veeorg is in fact a dual space isomorphic to . Furthermore, we answer an open problem from the literature by showing that there exists a superreflexive space, in the form of a renorming of , with a ‐point. Building on these two results...

We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson's property (C), Talponen's Countable Separation Property, or being a Gâteaux differentiability space. On the other hand, we single out more general properties where this equivalence fails. In particular, th...

We introduce relative versions of Daugavet-points and the Daugavet property, where the Daugavet-behavior is localized inside of some supporting slice. These points present striking similarities with Daugavet-points, but lie strictly between the notions of Daugavet- and $\Delta$-points. We provide a geometric condition that a space with the Radon--N...

We show that the Lipschitz-free space with the Radon--Nikod\'{y}m property and a Daugavet point recently constructed by Veeorg is in fact a dual space isomorphic to $\ell_1$. Furthermore, we answer an open problem from the literature by showing that there exists a superreflexive space, in the form of a renorming of $\ell_2$, with a $\Delta$-point....

For a complete metric space $M$, we define the notion of a convex integral of molecules in the Lipschitz-free space $\mathcal{F}(M)$ based on the de Leeuw representation of elements of its bidual $\mathcal{F}(M)^{**}$. Using optimal transport theory, we show that convex integrals of molecules are determined by cyclical monotonicity of their support...

One of the biggest challenges of whole-body scanners for Positron Emission Tomography is the correction of the scatter fraction, meaning the amount of false coincidences where one of the two 511-keV gammas has interacted in the patient's body and has changed its original direction. One way to overcome this difficulty is to use the scanner energy re...

New detector approaches in Positron Emission Tomography imaging will play an important role in reducing costs, lowering administered radiation doses, and improving overall performance. PETALO employs liquid xenon as the active scintillating medium and UV-sensitive silicon photomultipliers for scintillation readout. The scintillation time in liquid...

From the retraction notice: The editors of Proceedings of the Royal Society of Edinburgh Section A: Mathematics have retracted the following article because it was withdrawn from the journal by the authors on 24 September 2020, and its publication in this journal on 8 December 2021 was accidental. Due to an administrative error on the part of the...

New detector approaches in Positron Emission Tomography imaging will play an important role in reducing costs, lowering administered radiation doses, and improving overall performance. PETALO employs liquid xenon as the active scintillating medium and UV-sensitive silicon photomultipliers for scintillation readout. The scintillation time in liquid...

We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite-dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy consequences we derive several new and some known results. Th...

Let Lip0(M) be the space of Lipschitz functions on a complete metric space M that vanish at a base point. We prove that every normal functional in Lip0(M)* is weak* continuous; that is, in order to verify weak* continuity it suffices to do so for bounded monotone nets of Lipschitz functions. This solves a problem posed by N. Weaver. As an auxiliary...

We characterize compact metric spaces whose locally flat Lipschitz functions separate points uniformly as exactly those that are purely 1-unrectifiable, resolving a problem of Weaver. We subsequently use this geometric characterization to answer several questions in Lipschitz analysis. Notably, it follows that the Lipschitz-free space F(M) over a c...

We show that, for a separable and complete metric space M, the Lipschitz-free space F(M) embeds linearly and almost-isometrically into ℓ1 if and only if M is a subset of an R-tree with length measure 0. Moreover, it embeds isometrically if and only if the length measure of the closure of the set of branching points of M (taken in any minimal R-tree...

We prove that all extreme points of the unit ball of a Lipschitz-free space over a compact metric space have finite support. Combined with previous results, this completely characterizes extreme points and implies that all of them are also extreme points in the bidual ball. For the proof, we develop some properties of an integral representation of...

PETALO (a Positron Emission Tof Apparatus based on Liquid xenOn) is a new approach for Positron Emission Tomography scanners, based on liquid xenon. The PETALO detector aims at capturing the light produced by the scintillation in LXe taking advantage of its uniform response and continuity. This strategy will lead to a geometrical distortion free be...

Lipschitz-free spaces F(M) are canonical linearizations of arbitrary complete metric spaces M. More specifically, F(M) is the unique Banach space that contains an isometric copy of M that is linearly dense, and such that any Lipschitz mapping from M into some Banach space X extends to a bounded linear operator from F(M) into X. Those spaces are a v...

We analyze the relationship between Borel measures and continuous linear functionals on the space Lip0(M) of Lipschitz functions on a complete metric space M. In particular, we describe continuous functionals arising from measures and vice versa. In the case of weak* continuous functionals, i.e. members of the Lipschitz-free space F(M), measures on...

We consider convex series of molecules in Lipschitz-free spaces, i.e. elements of the form μ=∑nλnδxn−δynd(xn,yn) such that ‖μ‖=∑n|λn|. We characterise these elements in terms of geometric conditions on the points xn, yn of the underlying metric space, and determine when they are points of Gâteaux differentiability of the norm. In particular, we sho...

Let $\operatorname{Lip}_0(M)$ be the space of Lipschitz functions on a complete metric space $M$ that vanish at a base point. We show that every normal functional in $\operatorname{Lip}_0(M)^\ast$ is weak$^*$ continuous, answering a question by N. Weaver.

We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy consequences we derive several new and some known results. Th...

We show that the class of Lipschitz-free spaces over closed subsets of any complete metric space M is closed under arbitrary intersections, improving upon the previously known finite-diameter case. This allows us to formulate a general and natural definition of supports for elements in a Lipschitz-free space F(M). We then use this concept to study...

For a complete metric space M, we prove that the finitely supported extreme points of the unit ball of the Lipschitz-free space F(M) are precisely the elementary molecules (δ(p)−δ(q))/d(p, q) defined by pairs of points p, q in M such that the triangle inequality d(p, q) < d(p,r) + d(q, r) is strict for any r ∈ M different from p and q. To this end,...

We consider convex series of molecules in Lipschitz-free spaces, i.e. elements of the form $\mu=\sum_n \lambda_n \frac{\delta_{x_n}-\delta_{y_n}}{d(x_n,y_n)}$ such that $\|\mu\|=\sum_n |\lambda_n |$. We characterise these elements in terms of geometric conditions on the points $x_n$, $y_n$ of the underlying metric space, and determine when they are...

We show that the class of Lipschitz-free spaces over closed subsets of any complete metric space $M$ is closed under arbitrary intersections, improving upon the previously known finite-diameter case. This allows us to formulate a general and natural definition of supports for elements in a Lipschitz-free space $\mathcal F(M)$. We then use this conc...

In this note we study the Lipschitz-free space $\mathcal{F}(M)$ for a metric space $M$ which is a subset of an $\mathbb{R}$-tree. The main result states that $\mathcal{F}(M)$ embeds almost-isometrically into $\ell_1$ whenever the metric space $M$ is complete, separable and has length measure 0. If moreover $M$ is a proper metric space, then the con...

We show that, for a separable and complete metric space M, the Lipschitz-free space F(M) embeds linearly and almost-isometrically into ℓ1 if and only if M is a subset of an R-tree with length measure 0. Moreover, it embeds isometrically if and only if the length measure of the closure of the set of branching points of M (taken in any minimal R-tree...

We show that the class of Lipschitz-free spaces over closed subsets of any complete metric space M is closed under arbitrary intersections, improving upon the previously known finite-diameter case. This allows us to formulate a general and natural definition of supports for elements in a Lipschitz-free space F (M). We then use this concept to study...

PETALO Data Acquisition System

The spectroscopic performances of the new integrated ASIC (Application-Specific Integrated Circuit) preamplifiers for highly segmented silicon detectors have been evaluated with an early silicon detector prototype of the TRacking Array for light Charged Ejectiles (TRACE). The ASICS were mounted on a custom-designed PCB (Printed Circuit Board) and t...

A new neutron multiplicity filter NEDA, after a decade of design, R&D and construction, was employed in its first physics campaign with the AGATA spectrometer. Properties and performance of the array are discussed. 2019

The NEutron Detector Array, NEDA, will form the next generation neutron detection system that has been designed to be operated in conjunction with γ-ray arrays, such as the tracking-array AGATA, to aid nuclear spectroscopy studies. NEDA has been designed to be a versatile device, with high-detection efficiency, excellent neutron-γ discrimination, a...

We characterize preserved extreme points of the unit ball of Lipschitz-free spaces F(X) in terms of simple geometric conditions on the underlying metric space (X,d). Namely, the preserved extreme points are the elementary molecules corresponding to pairs of points p,q in X such that the triangle inequality d(p,q)≤d(p,r)+d(q,r) is uniformly strict f...

For a complete metric space $M$, we prove that the finitely supported extreme points of the unit ball of the Lipschitz-free space $\mathcal{F}(M)$ are precisely the elementary molecules $(\delta(p)-\delta(q))/d(p,q)$ defined by pairs of points $p,q$ in $M$ such that the triangle inequality $d(p,q)<d(p,r)+d(q,r)$ is strict for any $r\in M$ different...

This work presents a multichannel IC architecture which is able to process and digitize simultaneous current pulses in every input channel with no deadtime. The analog to digital conversion is performed in two steps: 6 MSBs are quantized by the Charge Pulse System (CPS) and 8 LSBs are obtained from a later ADC for a total of 14 ENOB at the output....

The NEutron Detector Array (NEDA) project aims at the construction of a new high-efficiency compact neutron detector array to be coupled with large \( \gamma\)-ray arrays such as AGATA. The application of NEDA ranges from its use as selective neutron multiplicity filter for fusion-evaporation reaction to a large solid angle neutron tagging device....

Positron Emission Tomography (PET) is a non-invasive nuclear medical imaging modality that makes it possible to observe the distribution of metabolic substances within a patient's body after marking them with radioactive isotopes and arranging an annular scanner around him in order to detect their decays. The main applications of this technique are...

The new TRacking Array for light Charged particle Ejectiles (TRACE) detector system requires monitorization and sampling of all pulses in a large number of channels with very strict space and power consumption restrictions for the front-end electronics and cabling. Its readout system is to be based on analog memory ASICs with 64 channels each that...

In the optimization of artificial neural networks (ANNs) via evolutionary algorithms and the implementation of the necessary training for the objective function, there is often a trade-off between efficiency and flexibility. Pure software solutions on general-purpose processors tend to be slow because they do not take advantage of the inherent para...

A thermoelectric micro generator able to harvest thermal energy and produce electrical power has been developed by research groups of CSIC and Universitat Politècnica de València. The generator consists of P-N semiconductor junctions and a structure with through hole connections which allows for building thermocouples along 3 dimensions.

A DAQ architecture for a PET system is presented that focuses on modularity, scalability and reusability. The system defines two basic building blocks: data acquisitors and concentrators, which can be replicated in order to build a complete DAQ of variable size. Acquisition modules contain a scintillating crystal and either a position-sensitive pho...

When implementing an artificial neural networks (ANNs) will need to know the topology and initial weights of each synaptic connection. The calculation of both variables is much more expensive computationally. This paper presents a scalable experimental platform to accelerate the training of ANN, using genetic algorithms and embedded systems with ha...

Improving timing resolution in positron emission tomography (PET), thus having fine time information of the detected pulses, is important to increase the reconstructed images signal to noise ratio (SNR) [1]. In the present work, an integrated circuit topology for time extraction of the incoming pulses is evaluated. An accurate simulation including...

AMIC architecture has been introduced in previous works in order to provide a generic and expandable solution for implementing large number of outputs SiPM array/PMT detectors. The underlying idea in AMIC architecture is to calculate the moments of the detected light distribution in an analog fashion. These moments provide information about energy,...

Scintillator based photodetectors tend to increase the number of output signals in order to improve spatial and energy resolutions. AMIC architecture was introduced in previous works as an alternative to traditional charge division front-ends. This novel architecture not only allowed to reduce the number of signals to be acquired but also provided...

A DAQ architecture for a PET system is presented that focuses on modularity, scalability and reusability. The system defines two basic building blocks: data acquisitors and concentrators, which can be replicated in order to build a complete DAQ of variable size. Acquisition modules contain a scintillating crystal and either a PSPMT or a SiPM array....

Current PET systems with fully digital trigger rely on early digitization of detector signals and the use of digital processors, usually FPGAs, for recognition of valid gamma events on single detectors. Timestamps are assigned and later used for coincidence analysis. In order to maintain a decent timing resolution for events detected on different a...

Coincidence time resolution is one of the most important issues in PET detectors. Improving this resolution is required to increase the noise equivalent count rate (NECR) that reduces the noise in the reconstructed images. The aim of this work is to evaluate the behavior and time resolution of different proposed time pick-off algorithms in order to...

A novel CMOS integrated front-end architecture is presented throughout this paper. It is designed to be used with detectors based on continuous scintillation crystals plus position sensitive photomultiplier. Its structure aims at carrying out an analog computation which extracts fundamental information of the detected event. This fact allows us to...

In this article we introduce AMIC (Analog Moments Integrated Circuit), a novel analog Application Specific Integrated Circuit (ASIC) front-end for Positron Emission Tomography (PET) applications. Its working principle is based on mathematical analysis of light distribution through moments calculation. Each moment provides useful information about l...

Current PET systems with fully digital trigger rely on early digitization of detector signals and the use of digital processors, usually FPGAs, for recognition of valid gamma events on single detectors. Timestamps are assigned and later used for coincidence analysis. Good timing resolution is important, allowing better rejection of singles and lead...

A novel CMOS integrated front-end architecture is presented which enables a direct expansion of its number of inputs. This front-end is designed to be used with detectors based on continuous scintillation crystals plus position sensitive photomultiplier. Its structure aims at carrying out an analog computation which extracts fundamental information...

Coincidence time resolution is one of the most important issues in PET detectors. Improving this resolution is required to increase true event coincidence rates that reduce the noise in the reconstructed images. The aim of this work is to obtain a better time resolution for our PET system designing the most appropriate time extraction digital algor...

FPGAs offer a promising platform for the implementation of artificial neural networks (ANNs) and their training, combining the use of custom optimized hardware with low cost and fast development time. However, purely hardware realizations tend to focus on throughput, resorting to restrictions on applicable network topology or low-precision data rep...

Implementations of Artificial Neural Networks (ANNs) and their training often have to deal with a trade-off between efficiency and flexibility. Pure software solutions on general-purpose processors tend to be slow because they do not take advantage of the inherent parallelism, whereas hardware realizations usually rely on optimizations that reduce...

The center of gravity algorithm leads to strong artifacts for gamma-ray imaging detectors that are based on monolithic scintillation crystals and position sensitive photo-detectors. This is a consequence of using the centroids as position estimates. The fact that charge division circuits can also be used to compute the standard deviation of the sci...

Traditionally, the most popular technique to predict the impact position of gamma photons on a PET detector has been Anger's logic. However, it introduces nonlinearities that compress the light distribution, reducing the useful field of view and the spatial resolution, especially at the edges of the scintillator crystal. In this work, we make use o...

PET systems need good time resolution to improve the true event rate, random event rejection, and pile-up rejection. In this study we propose a digital procedure for this task using a low pass filter interpolation plus a Digital Constant Fraction Discriminator (DCFD). We analyzed the best way to implement this algorithm on our dual head PET system...

A novel design for an inexpensive depth of interaction capable detector for γ-ray imaging has been developed. The design takes advantage of the strong correlation between the width of the scintillation light distribution in monolithic crystals and the interaction depth of γ-rays. We present in this work an inexpensive modification of the commonly u...

New digital PET detectors are based in an early digitalization of the detector signals. In these systems, digital signal processing (with FPGAs, DSPs or both) is applied to extract the information from the detected events. Algorithms adapted to the available hardware resources should be proposed to detect gamma-ray energy, impact position and event...

The backpropagation algorithm used for the training of Multilayer Perceptrons (MLPs) has a high degree of parallelism and is therefore well-suited for hardware implementation on an ASIC or FPGA. However, most implementations are lacking in generality of application, either by limiting the range of trainable network topologies or by resorting to fix...

Current testbenches for nuclear imaging devices aim to simulate only a single stage of the system at a time. This approach is useful in early design stages where accuracy is not necessary. However, it would be desirable that different tools could be combined to achieve more detailed simulations. In this work, a high precision testbench is presented...

Positron Emission Tomography (PET) is a radiotracer imaging technique based on the administration (typically by injection) of compounds labelled with positron emitting radionuclides to a patient under study. When the radio-isotope decays, it emits a positron, which travels a short distance before annihilating with an electron. This annihilation pro...

The correct determination of the position of incident photons is a crucial issue in PET imaging.In this paper we study the use of Neural Networks (NNs) for position estimation of photons impinging on gamma-ray detector modules for PET cameras based on continuous scintillators and Multi-Anode Photomultiplier Tubes (MA-PMTs). We have performed a thor...

Current testbenches for nuclear imaging devices aim to simulate only a single stage of the system at a time. This approach is useful in early design stages where accuracy is not necessary. However, it would be desirable that different tools could be combined to achieve more detailed simulations. In this work, we present a high precision testbench t...

This paper studies the use of Neural Networks (NNs) for estimating the position of impinging photons in gamma ray detector modules for PET cameras based on continuous scintillators and Multi-Anode Photomultiplier Tubes (MA-PMTs). The detector under study is composed of a 49×49×10 mm³ continuous slab of LSO coupled to a flat panel H8500 M...

This paper studies the use of Neural Networks (NNs) for position estimation in PET -ray detectors. We focus on bidimensional positioning for sensors based on scintillators and Position Sensitive Photomultiplier Tubes (PS-PMTs). Concretely, the detector under study is composed of a 49 ◊ 49 ◊ 10 mm3 LSO continuous crystal optically coupled to the fla...

This paper studies the use of neural networks (NNs) for estimating the position of impinging photons in 7 ray detector modules for PET cameras based on multi-anode photomultiplier tubes (MA-PMTs). The detector under study is composed of a 49 × 49 × 10 mm³ continuous slab of LSO coupled to a flat panel H8500 MA-PMT. Four digitized signals...