Several open problems in operator theory

We report on the meeting Operators in Banach spaces recently held in Castro Urdiales as a homage to Pietro Aiena, and we collect the questions proposed by the participants during the Open Problems Session.Ministerio de Ciencia e Innovación (MICINN) de España. Grant MTM2011-2653 y MTM2010-20190.peerReviewe

Expected exponential loss for gaze-based video and volume ground truth annotation

Many recent machine learning approaches used in medical imaging are highly reliant on large amounts of image and ground truth data. In the context of object segmentation, pixel-wise annotations are extremely expensive to collect, especially in video and 3D volumes. To reduce this annotation burden, we propose a novel framework to allow annotators to simply observe the object to segment and record where they have looked at with a \$200 eye gaze tracker. Our method then estimates pixel-wise probabilities for the presence of the object throughout the sequence from which we train a classifier in semi-supervised setting using a novel Expected Exponential loss function. We show that our framework provides superior performances on a wide range of medical image settings compared to existing strategies and that our method can be combined with current crowd-sourcing paradigms as well.Comment: 9 pages, 5 figues, MICCAI 2017 - LABELS Worksho

A large sample analysis of European rivers on seasonal river flow correlation and its physical drivers

The geophysical and hydrological processes governing river flow formation exhibit persistence at several timescales, which may manifest itself with the presence of positive seasonal correlation of streamflow at several different time lags. We investigate here how persistence propagates along subsequent seasons and affects low and high flows. We define the high-flow season (HFS) and the low-flow season (LFS) as the 3-month and the 1-month periods which usually exhibit the higher and lower river flows, respectively. A dataset of 224 rivers from six European countries spanning more than 50 years of daily flow data is exploited. We compute the lagged seasonal correlation between selected river flow signatures, in HFS and LFS, and the average river flow in the antecedent months. Signatures are peak and average river flow for HFS and LFS, respectively. We investigate the links between seasonal streamflow correlation and various physiographic catchment characteristics and hydro-climatic properties. We find persistence to be more intense for LFS signatures than HFS. To exploit the seasonal correlation in the frequency estimation of high and low flows, we fit a bi-variate meta-Gaussian probability distribution to the selected flow signatures and average flow in the antecedent months in order to condition the distribution of high and low flows in the HFS and LFS, respectively, upon river flow observations in the previous months. The benefit of the suggested methodology is demonstrated by updating the frequency distribution of high and low flows one season in advance in a real-world case. Our findings suggest that there is a traceable physical basis for river memory which, in turn, can be statistically assimilated into high- and low-flow frequency estimation to reduce uncertainty and improve predictions for technical purposes

Topological and spectral properties of random digraphs

We investigate some topological and spectral properties of Erd\H{o}s-R\'{e}nyi (ER) random digraphs $D(n,p)$. In terms of topological properties, our primary focus lies in analyzing the number of non-isolated vertices $V_x(D)$ as well as two vertex-degree-based topological indices: the Randi\'c index $R(D)$ and sum-connectivity index $\chi(D)$. First, by performing a scaling analysis we show that the average degree $\langle k \rangle$ serves as scaling parameter for the average values of $V_x(D)$, $R(D)$ and $\chi(D)$. Then, we also state expressions relating the number of arcs, spectral radius, and closed walks of length 2 to $(n,p)$, the parameters of ER random digraphs. Concerning spectral properties, we compute six different graph energies on $D(n,p)$. We start by validating $\langle k \rangle$ as the scaling parameter of the graph energies. Additionally, we reformulate a set of bounds previously reported in the literature for these energies as a function $(n,p)$. Finally, we phenomenologically state relations between energies that allow us to extend previously known bounds

Scattering at the Anderson transition: Power--law banded random matrix model

We analyze the scattering properties of a periodic one-dimensional system at criticality represented by the so-called power-law banded random matrix model at the metal insulator transition. We focus on the scaling of Wigner delay times $\tau$ and resonance widths $\Gamma$. We found that the typical values of $\tau$ and $\Gamma$ (calculated as the geometric mean) scale with the system size $L$ as $\tau^{\tiny typ}\propto L^{D_1}$ and $\Gamma^{\tiny typ} \propto L^{-(2-D_2)}$, where $D_1$ is the information dimension and $D_2$ is the correlation dimension of eigenfunctions of the corresponding closed system.Comment: 6 pages, 8 figure

Pool-Type Fishway Design for a Potamodromous Cyprinid in the Iberian Peninsula: The Iberian Barbel—Synthesis and Future Directions

M.B., J.R.R., and J.P. would like to acknowledge support from the Spanish Ministry of Economy and Competitiveness (Ministerio de Economía y Competitividad) (Ref. CGL2012-34688) and thank the CITEEC (Centro de Innovación Tecnolóxica en Edificación e Enxeñería Civil) of the University of A Coruña and the Center for Hydrographic Studies of CEDEX for their ongoing collaboration in this research field. Finally, the authors want to thank the three anonymous reviewers for their comments and suggestions that improved this manuscript.The Iberian barbel (Luciobarbus bocagei) is one of the most common cyprinids in the Iberian Peninsula, whose migratory routes are often hampered by anthropogenic barriers. Fishways might be an effective mitigation measure if they integrate designed operational characteristics that account for the biomechanical requirements of this species. Understanding the flow conditions inside the fishway, and how barbel responds to the hydrodynamics of the flow is imperative to improve free migratory routes with minimum energetic cost associated. Herein, we analyze and synthesize the main findings of research on pool-type fishways for upstream passage of the Iberian barbel and derive recommendations of design criteria for pool-type fishways for this species and others of similar biomechanics capacities. Ultimately, we identify research needs to improve upstream passage of this species.A.T.S. was supported by the Norwegian Research Centre for Hydropower Technology—HydroCen (Project No. 257588); M.B. was funded from EU’s Horizon 2020 Programme under Marie Sklodowska-Curie Grant Agreement 754446 and UGR Research and Knowledge Transfer Fund—Athenea3i; and J.M.S. was supported by national funds via FCT under the CEEC Institucional 2018 (Ref. 2/ISA/FCT/2018). Forest Research Centre (CEF) is a research unit funded by Fundação para a Ciência e a Tecnologia I.P. (FCT), Portugal (UIDB/00239/2020)

Step height standards based on self-assembly for 3D metrology of biological samples

Modern microscopes and profilometers such as the coherence scanning interferometer (CSI) approach sub-nm precision in height measurements. Transfer standards at all measured size scales are needed to guarantee traceability at any scale and utilize the full potential of these instruments, but transfer standards with similar characteristics upon reflection to those of the measured samples are preferred. This is currently not the case for samples featuring dimensions of less than 10 nm and for biosamples with different optical charasteristics to silicon, silica or metals. To address the need for 3D images of biosamples with traceable dimensions, we introduce a transfer standard with dimensions guaranteed by natural self-assembly and a material that is optically similar to that in typical biosamples. We test the functionality of these transfer standards by first calibrating them using an atomic force microscope (AFM) and then using them to calibrate a CSI. We investigate whether a good enough calibration accuracy can be reached to enable a useful calibration of the CSI system. The result is that the calibration uncertainty is only marginally increased due to the samplePeer ReviewedPostprint (published version

Phoneutria depilata (Araneae: Ctenidae) in Panama: report of a bite case in Bocas del Toro province, notes on distribution and public health relevance

Phoneutria depilata is considered Panama´s most relevant spider species due to its aggressivity and venom. In this article, we described a case of P. depilata bite in a woman from Bocas del Toro Province, Panama. The symptoms included severe pain, swelling in the bite site, palpitation of submandibular ganglia, abundant salivation, tachycardia, and a sensation of "electricity". The swelling and pain lasted almost two days and three days, respectively. In addition, we present the geographical distribution of this spider species in Panama