New zero free regions for the derivatives of the Riemann zeta function

The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the right half-plane where these derivatives cannot have any zeros; and then, in the rare regions of the complex plane that do contain zeros of the k-th derivative of the zeta function, we describe a unexpected phenomenon, which implies great regularities in their zero distributions. In particular, we prove sharp estimates for the number of zeros in each of these new critical strips, and we explain how they converge, in a very precise, periodic fashion, to their central, critical lines, as k increases. This not only shows that the zeros are not randomly scattered to the right of the line Re(s)=1, but that, in many respects, their two-dimensional distribution eventually becomes much simpler and more predictable than the one-dimensional behavior of the zeros of the zeta function on the line Re(s)=1/2

Understanding and Comparing Deep Neural Networks for Age and Gender Classification

Recently, deep neural networks have demonstrated excellent performances in recognizing the age and gender on human face images. However, these models were applied in a black-box manner with no information provided about which facial features are actually used for prediction and how these features depend on image preprocessing, model initialization and architecture choice. We present a study investigating these different effects. In detail, our work compares four popular neural network architectures, studies the effect of pretraining, evaluates the robustness of the considered alignment preprocessings via cross-method test set swapping and intuitively visualizes the model's prediction strategies in given preprocessing conditions using the recent Layer-wise Relevance Propagation (LRP) algorithm. Our evaluations on the challenging Adience benchmark show that suitable parameter initialization leads to a holistic perception of the input, compensating artefactual data representations. With a combination of simple preprocessing steps, we reach state of the art performance in gender recognition.Comment: 8 pages, 5 figures, 5 tables. Presented at ICCV 2017 Workshop: 7th IEEE International Workshop on Analysis and Modeling of Faces and Gesture

Unmasking Clever Hans Predictors and Assessing What Machines Really Learn

Current learning machines have successfully solved hard application problems, reaching high accuracy and displaying seemingly "intelligent" behavior. Here we apply recent techniques for explaining decisions of state-of-the-art learning machines and analyze various tasks from computer vision and arcade games. This showcases a spectrum of problem-solving behaviors ranging from naive and short-sighted, to well-informed and strategic. We observe that standard performance evaluation metrics can be oblivious to distinguishing these diverse problem solving behaviors. Furthermore, we propose our semi-automated Spectral Relevance Analysis that provides a practically effective way of characterizing and validating the behavior of nonlinear learning machines. This helps to assess whether a learned model indeed delivers reliably for the problem that it was conceived for. Furthermore, our work intends to add a voice of caution to the ongoing excitement about machine intelligence and pledges to evaluate and judge some of these recent successes in a more nuanced manner.Comment: Accepted for publication in Nature Communication

Signatures of a Bardeen-Cooper-Schrieffer Polariton Laser

Microcavity exciton polariton systems can have a wide range of macroscopic quantum effects that may be turned into better photonic technologies. Polariton Bose-Einstein condensation (BEC) and photon lasing have been widely accepted in the limits of low and high carrier densities, but identification of the expected Bardeen-Cooper-Schrieffer (BCS) state at intermediate densities remains elusive. While all three phases feature coherent photon emission, essential differences exist in their matter media. Most studies to date characterize only the photon field. Here, using a microcavity with strong- and weak-couplings co-existing in orthogonal linear polarizations, we directly measure the electronic gain in the matter media of a polariton laser, demonstrating a BCS-like polariton laser above the Mott transition density. Theoretical analysis reproduces the absorption spectra and lasing frequency shifts, revealing an electron distribution function characteristic of a polariton BCS state but modified by incoherent pumping and dissipation

A Randomized Controlled Trial of Glucose versus Amylase Resistant Starch Hypo-Osmolar Oral Rehydration Solution for Adult Acute Dehydrating Diarrhea

Background: Reduction of gross diarrhea rate in excess of that seen over time with intravenous therapy and appropriate antibiotics is not usually achieved by oral glucose-electrolyte rehydration therapy for cholera and cholera-like diarrheas. Methodology and Principal Findings: This prospective randomized clinical trial at a tertiary referral hospital in southern India was undertaken to determine whether amylase resistant starch, substituting for glucose in hypo-osmolar oral rehydration solution, would reduce diarrhea duration and weight in adults with acute severe dehydrating diarrhea. 50 adult males with severe watery diarrhea of less than three days' duration and moderate to severe dehydration were randomized to receive hypo-osmolar ORS (HO-ORS) or HO-ORS in which amylase resistant high amylose maize starch 50g/L substituted for glucose (HAMS-ORS). All remaining therapy followed standard protocol. Duration of diarrhea (ORS commencement to first formed stool) in hours was significantly shorter with HAMS-ORS (median 19, IQR 10-28) compared to HO-ORS (median 42, IQR 24-50) (Bonferroni adjusted P, P-adj < 0.001). Survival analysis (Kaplan-Meier) showed faster recovery from diarrhea in the HAMS-ORS group (P < 0.001, log rank test). Total diarrhea fecal weight in grams (median, IQR) was not significantly lower in the HAMS-ORS group (2190, 1160-5635) compared to HO-ORS (5210, 2095-12190) (P-adj = 0.08). However, stool weight at 13-24 hours (280, 0-965 vs. 1360, 405-2985) and 25-48 hours (0, 0-360 vs. 1080, 55-3485) were significantly lower in HAMS-ORS compared to HO-ORS group (Padj = 0.048 and P = 0.012, respectively). ORS intake after first 24 hours was lower in the HAMS-ORS group. Subgroup analysis of patients with culture isolates of Vibrio cholerae indicated similar significant differences between the treatment groups. Conclusions: Compared to HO-ORS, HAMS-ORS reduced diarrhea duration by 55% and significantly reduced fecal weight after the first 12 hours of ORS therapy in adults with cholera-like diarrhea

Symmetry-allowed phase transitions realized by the two-dimensional fully frustrated XY class

A 2D Fully Frustrated XY(FFXY) class of models is shown to contain a new groundstate in addition to the checkerboard groundstates of the standard 2D FFXY model. The spin configuration of this additional groundstate is obtained. Associated with this groundstate there are additional phase transitions. An order parameter accounting for these new transitions is proposed. The transitions associated with the new order parameter are suggested to be similar to a 2D liquid-gas transition which implies Z_2-Ising like transitions. This suggests that the class of 2D FFXY models belongs within a U(1) x Z_2 x Z_2-designation of possible transitions, which implies that there are seven different possible single and combined transitions. MC-simulations for the generalized fully frustrated XY (GFFXY) model on a square lattice are used to investigate which of these possibilities can be realized in practice: five of the seven are encountered. Four critical points are deduced from the MC-simulations, three consistent with central charge c=3/2 and one with c=1. The implications for the standard 2D FFXY-model are discussed in particular with respect to the long standing controversy concerning the characteristics of its phase transitions.Comment: 8 pages, 8 figure