Completing Diophantus, De polygonis numeris, prop. 5

AbstractThe last proposition of Diophantus’ De polygonis numeris, inquiring the number of ways that a number can be polygonal and apparently aiming at “simplifying” the definitory relation established by Diophantus himself, is incomplete. Past completions of this proposition are reported in detail and discussed, and a new route to a “simplified” relation is proposed, simpler, more transparent and more “Greek looking” than the others. The issue of the application of such a simplified relation to solving the problem set out by Diophantus is also discussed in full detail

High Sensitivity Photodetector for Photon-Counting Applications

In the last years, there has been a large development of low-light applications, and many of them are based on photon counting using single-photon detectors (SPDs). These are very sensitive detectors typically with an internal gain. The first candidate SPD was the photomultiplier tube (PMT), reaching a very high gain (~106), but there have been a large development of many other solutions, like solid-state solutions. Among them, single-photon avalanche diodes (SPADs) have been used in spectroscopy, florescence imaging, etc., particularly for their good detection efficiency and time resolution (tens of picoseconds). SPADs have been developed in silicon and III–V materials, for the NIR wavelength range. SPADs can be used as single high-performance pixels, or in arrays. SPAD arrays have imaging capabilities, with high sensitivity. Another kind of array is the silicon photomultiplier (SiPM), where all the pixels are connected to a common anode and a common cathode. SiPMs are used in nuclear medicine, physics experiments, quantum-physics experiments, light detection and ranging (LIDAR), etc., due to their high detection efficiency combined with large sensitive areas, and high dynamic range. SiPMs with many small cells present several advantages and nowadays the SPAD pitch can be reduced down to 5 μm

Compact Quantum Random Number Generator with Silicon Nanocrystals Light Emitting Device Coupled to a Silicon Photomultiplier

A small-sized photonic quantum random number generator, easy to be implemented in small electronic devices for secure data encryption and other applications, is highly demanding nowadays. Here, we propose a compact configuration with Silicon nanocrystals large area light emitting device (LED) coupled to a Silicon photomultiplier to generate random numbers. The random number generation methodology is based on the photon arrival time and is robust against the non-idealities of the detector and the source of quantum entropy. The raw data show high quality of randomness and pass all the statistical tests in national institute of standards and technology tests (NIST) suite without a post-processing algorithm. The highest bit rate is 0.5 Mbps with the efficiency of 4 bits per detected photon

Modeling Approaches Reveal New Regulatory Networks in <i>Aspergillus fumigatus</i> Metabolism

Systems biology approaches are extensively used to model and reverse-engineer gene regulatory networks from experimental data. Indoleamine 2,3-dioxygenases (IDOs)—belonging in the heme dioxygenase family—degrade l-tryptophan to kynurenines. These enzymes are also responsible for the de novo synthesis of nicotinamide adenine dinucleotide (NAD+). As such, they are expressed by a variety of species, including fungi. Interestingly, Aspergillus may degrade l-tryptophan not only via IDO but also via alternative pathways. Deciphering the molecular interactions regulating tryptophan metabolism is particularly critical for novel drug target discovery designed to control pathogen determinants in invasive infections. Using continuous time Bayesian networks over a time-course gene expression dataset, we inferred the global regulatory network controlling l-tryptophan metabolism. The method unravels a possible novel approach to target fungal virulence factors during infection. Furthermore, this study represents the first application of continuous-time Bayesian networks as a gene network reconstruction method in Aspergillus metabolism. The experiment showed that the applied computational approach may improve the understanding of metabolic networks over traditional pathways

Breaking the rules of time-domain diffuse optics: working with 1 cm2 SiPM and well-beyond the single-photon statistics

Time domain diffuse optics (TD-DO) relies on the injection of ps laser pulses and on the collection of the arrival times of scattered photons. To reach the ultimate limits of the technique (allowing to investigate even structures at depth &gt;5 cm), a large area detector is needed. To this extent, we realized and present a new silicon photomultiplier featuring a 1 cm2 area. To the best of our knowledge, it represents the largest detector ever proposed for TD-DO and shows a light harvesting capability which is more than 1 decade larger than the state-of-the-art technology system. To assess its suitability for TDDO measurements, we tested the detector with several procedures from shared protocols (BIP, nEUROPt and MEDPHOT). However, the light harvesting capability of a detector with large area can be proficiently exploited only if coupled to timing electronics working in sustained count-rate CR (i.e., well above the single photon statistics). For this reason, we study the possibility to work in a regime where (even more than) one photon per laser pulse is detected (i.e., more than 100% laser repetition rate) exploiting in-silico technology. The results show that the possibility to use sustained count-rate represents a dramatic improvement in the number of photons detected with respect to current approaches (where count-rate of 1-5% of the laser repetition rate are used) without significant losses in the measurement accuracy. This represents a new horizon for TD-DO measurements, opening the way to new applications (e.g., optical investigation of the lung or monitoring of fast dynamics never studied before)

Cryogenic Characterization of FBK HD Near-UV Sensitive SiPMs

We report on the characterization of near-ultraviolet high density silicon photomultiplier (\SiPM) developed at Fondazione Bruno Kessler (\FBK) at cryogenic temperature. A dedicated setup was built to measure the primary dark noise and correlated noise of the \SiPMs\ between 40 and 300~K. Moreover, an analysis program and data acquisition system were developed to allow the precise characterization of these parameters, some of which can vary up to 7 orders of magnitude between room temperature and 40~K. We demonstrate that it is possible to operate the \FBK\ near-ultraviolet high density \SiPMs\ at temperatures lower than 100~K with a dark rate below 0.01 cps/mm$^2$ and total correlated noise probability below 35\% at an over-voltage of 6~V. These results are relevant for the development of future cryogenic particle detectors using \SiPMs\ as photosensors

Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices

Optimization of Pinned Photodiode Pixels for High-Speed Time of Flight Applications

We discuss optimizations of pinned photodiode (PPD) pixels for indirect time of flight sensors. We focus on the transfer-gate and dumping gate regions optimization, on the PPD dimension and shape to assure fast lateral charge transfer and on the epitaxial layer thickness for a good tradeoff between fast vertical charge transfer and high quantum efficiency at near infrared region. The overall performance of the pixel is quantified by the demodulation contrast of the pixel at specific frequencies. The operation frequency of the device is determined by the required ambiguity range of the application and the required distance noise. In order to reach a reasonable distance noise, the pixel needs to allow modulation frequencies up to 100 MHz. In this paper, we present TCAD simulation and experimental data on demodulation contrast, impulse response time, and quantum efficiency of $10 \times 10\,\,\mu \text{m}$ pixels. We introduce a setup for impulse response measurement and we compare this to the demodulation contrast. We also discuss the optimization of the dump gate and dump diffusion. With the best pixel we measured a quantum efficiency of about 45% at 850 nm, a demodulation contrast of 47% at 80 MHz, and an impulse response time < 5 ns