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We investigate here the sign uncertainty phenomenon for bandlimited functions, with a competing condition given by integration with respect to a general measure. Our main result provides a framework related to the theory of de Branges spaces of entire functions, that allows one to find the sharp constants and classify the extremizers in a broad range of situations. We discuss an application in number theory, in connection to bounds for zeros of $L$-functions., Comment: 26 pages

By means of a Fourier optimization framework, we improve the current asymptotic bounds under GRH for two classical problems in number theory: the problem of estimating the least quadratic non-residue modulo a prime, and the problem of estimating the least prime in an arithmetic progression., Comment: 25 pages, 4 figures

We consider a variant of a problem first introduced by Hughes and Rudnick (2003) and generalized by Bernard (2015) concerning conditional bounds for small first zeros in a family of $L$-functions. Here we seek to estimate the size of the smallest intervals centered at a low-lying height for which we can guarantee the existence of a zero in a family of $L$-functions. This leads us to consider an extremal problem in analysis which we address by applying the framework of de Branges spaces, introduced in this context by Carneiro, Chirre, and Milinovich (2022)., Comment: 26 pages, 1 figure

We characterize cofibrant objects in the category of functors indexed in a filtered poset and we show that these objects are acyclic. As a consequence, we show that Mackey functors over posets are also acyclic, where we define this type of Mackey functors mimicking the classical notion. As application, we study homotopy colimits over posets and we give a homology decomposition for the classifying space of the Bianchi group $\Gamma_1$.

Assuming the Riemann hypothesis, we improve the current upper and lower bounds for the average value of Montgomery's function $F(\alpha, T)$ over long intervals by means of a Fourier optimization framework. The function $F(\alpha, T)$ is often used to study the pair correlation of the non-trivial zeros of the Riemann zeta-function. Two ideas play a central role in our approach: (i) the introduction of new averaging mechanisms in our conceptual framework and (ii) the full use of the class of test functions introduced by Cohn and Elkies for the sphere packing bounds, going beyond the usual class of bandlimited functions. We conclude that such an average value, that is conjectured to be $1$, lies between $0.9303$ and $1.3208$. Our Fourier optimization framework also yields an improvement on the current bounds for the analogous problem concerning the non-trivial zeros in the family of Dirichlet $L$-functions., Comment: 14 pages, 1 figure

Our automated reaction discovery program, AutoMeKin, has been utilized to investigate the formation of glycolonitrile (HOCH$_{2}$CN) in the gas phase under the low temperatures of the interstellar medium (ISM). The feasibility of a proposed pathway depends on the absence of barriers above the energy of reactants and the availability of the suggested precursors in the ISM. Based on these criteria, several radical-radical reactions and a radical-molecule reaction have been identified as viable formation routes in the ISM. Among the radical-radical reactions, OH+CH$_{2}$CN appears to be the most relevant, considering the energy of the radicals and its ability to produce glycolonitrile in a single step. However, our analysis reveals that this reaction produces hydrogen isocyanide (HNC) and formaldehyde (CH$_{2}$O), with rate coefficients ranging from (7.3-11.5)$\times$10$^{-10}$ cm$^3$ molecule$^{-1}$ s$^{-1}$ across the temperature range of 10-150 K. This finding is particularly interesing given the persistently unexplained overabundance of hydrogen isocyanide in the ISM. Among the radical-molecule reactions investigated, the most promising one is OH+CH$_{2}$CNH, which forms glycolonitrile and atomic hydrogen with rate coefficients in the range (0.3-6.6)$\times$10$^{-10}$ cm$^3$ molecule$^{-1}$ s$^{-1}$ within the 10-150 K temperature range. Our calculations indicate that the formation of both hydrogen isocyanide and glycolonitrile is efficient under the harsh conditions of the ISM.

In this paper we address the problem of estimating the operator norm of the embeddings between multidimensional weighted Paley-Wiener spaces. These can be equivalently thought as Fourier uncertainty principles for bandlimited functions. By means of radial symmetrization mechanisms, we show that such problems can all be shifted to dimension one. We provide precise asymptotics in the general case and, in some particular situations, we are able to identify the sharp constants and characterize the extremizers. The sharp constant study is actually a consequence of a more general result we prove in the setup of de Branges spaces of entire functions, addressing the operator given by multiplication by $z^k$, $k \in \mathbb{N}$. Applications to sharp higher order Poincar\'{e} inequalities and other related extremal problems are discussed., Comment: 43 pages

We prove Quillen's conjecture for finite simple unitary groups and obtain, as a consequence of the Aschbacher-Smith work, Quillen's conjecture for all odd primes.

The use of thin liquid films has expanded beyond lubrication and coatings, and into applications in actuators and adaptive optical elements. In contrast to their predecessors, whose dynamics can be typically captured by modelling infinite or periodic films, these applications are characterized by a finite amount of liquid in an impermeable domain. The global mass conservation constraint, together with common boundary conditions (e.g., pinning) create quantitatively and qualitatively different dynamics than those of infinite films. Mathematically, this manifests itself as a non-self-adjoint problem. This work presents a combined theoretical and experimental study for this problem. We provide a time-dependent closed-form analytical solution for the linearized non-self-adjoint system that arises from these boundary conditions. We highlight that, in contrast to self-adjoint problems, here special care should be given to deriving the adjoint problem to reconstruct the solution based on the eigenfunctions properly. We compare these solutions with those obtained for permeable and periodic boundary conditions, representing common models for self-adjoint thin-film problems. We show that while the initial dynamics are nearly identical, the boundary conditions eventually affect the film deformation as well as its response time. To experimentally illustrate the dynamics and to validate the theoretical model, we fabricated an experimental setup that subjects a thin liquid film to a prescribed normal force distribution through dielectrophoresis, and used high-frame-rate digital holography to measure the film deformation in real-time. The experiments agree well with the model and confirm that confined films exhibit different behaviour which could not be predicted by existing models., Comment: 16 pages, 6 figures

A FEM application for the accurate design of composite backing of ultrasonic transducers is presented. The idea is to obtain the dependence between the volume ratio of the tungsten powder in an epoxy matrix used as a backing and the final pulsed RF signal emitted by the backed transducer. An inhomogeneous material model for the backing was adopted instead of the classic complex geometrical FEM. The model was developed in Comsol 5.5 using two of its physics interfaces. The first based on classic FEM or continuous Galerkin for ultrasonic propagation in the backing and the second based on a discontinuous Galerkin option for fluid pulsed propagation. In this way it is possible to avoid the use of an impedance-based model. The calculations for the resulting bandwidth are good enough as predicted for Desilets for the 1D case by using the KLM circuital model. We worked in a 2D space, where the transducer face vibration is far away from the assumed piston-like considered by the unidimensional KLM model., Comment: 14 pages, 9 figures

It is well known that not every finite group arises as the full automorphism group of some group. Here we show that the situation is dramatically different when considering the category of partial groups, ${{\mathcal P}art}$, as defined by Chermak: given any group $H$ there exists infinitely many non isomorphic partial groups ${\mathbb M}$ such that $\operatorname{Aut}_{{\mathcal P}art}({\mathbb M})\cong H$. To prove this result, given any simple undirected graph $G$ we construct a partial group ${\mathbb P}(G)$, called the path partial group associated to $G$, such that $\operatorname{Aut}_{{\mathcal P}art}\big({\mathbb P}(G)\big)\cong \operatorname{Aut}_{{\mathcal G}raphs}(G)$. As a consequence, we solve the Kahn realizability problem in the category of simplicial sets.

We present a theoretical model and experimental demonstration of thin liquid film deformations due to a dielectric force distribution established by surface electrodes. We model the spatial electric field produced by a pair of parallel electrodes and use it to evaluate the stress on the interface through Maxwell stresses. By coupling this force with the Young-Laplace equation, we obtain the deformation of the interface. To validate our theory, we design an experimental setup which uses microfabricated electrodes to achieve spatial dielectrophoretic actuation of a thin liquid film, while providing measurements of microscale deformations through digital holographic microscopy. We characterize the deformation as a function of the electrode-pair geometry and film thickness, showing very good agreement with the model. Based on the insights from the characterization of the system, we pattern conductive lines of electrode pairs on the surface of a microfluidic chamber and demonstrate the ability to produce complex two-dimensional deformations. The films can remain in liquid form and be dynamically modulated between different configurations or polymerized to create solid structures with high surface quality., Comment: 14 pages and 7 figures in the main manuscript. 4 sections and 5 figures in the SI

We investigate the decline of infant mortality in 42 low and middle income countries (LMIC) using detailed micro data from 84 Demographic and Health Surveys. We estimate infant mortality risk for each infant in our data and develop a novel extension of Oaxaca decomposition to understand the sources of these changes. We find that the decline in infant mortality is due to a declining propensity for parents with given characteristics to experience the death of an infant rather than due to changes in the distributions of these characteristics over time. Our results suggest that technical progress and policy health interventions in the form of public goods are the main drivers of the the recent decline in infant mortality in LMIC.

In contrast to the commonly used spherical Janus particles, here we used engineered Janus particles that are fabricated using photolithography technique for precise control over their geometry and coated regions. Specifically, we studied a lollipop-shaped complex particle where its head is coated with gold while its tail is left bare. Due to their distinct electrical properties (i.e. electrical polarizability) the particle exhibits force equilibrium where opposite dielectrophoretic forces acting on its head and tail exactly cancel each other to yield a stable equilibrium position. This was realized in a quadrupolar electrode array where the equilibrium position of the engineered particle could be tuned by the frequency. This stands in contrast to the standard dielectrophoretic behavior where the particle shifts positions from either the center of the quad to the very edge of the electrodes when shifting from a negative to positive dielectrophoretic response, respectively. This opens new opportunities for positioning control of such complex particles for self-assembly, biosensing, biomimetic spermatozoa and more., Comment: 10 pages, 4 figures

We introduce {\em admissible collections} for a finite group $G$ and use them to prove that most of the finite classical groups in non-defining characteristic satisfy the {\em Quillen dimension at $p$ property}, a strong version of Quillen's conjecture, at a given odd prime divisor $p$ of $|G|$. Compared to the methods in \cite{AS1993}, our techniques are simpler., Comment: First Author supported by MEC grant MTM2016-78647-P and Junta de Andaluc\'ia grant FQM-213

We prove the Cartan-Eilenberg stable elements theorem and construct a Lyndon-Hochschild-Serre type spectral sequence for pro-fusion systems. As an application, we determine the continuous mod-$p$ cohomology ring of $\text{GL}_2(\mathbb{Z}_p)$ for any odd prime $p$., Comment: 19 pages, 4 figures

We study the properties of an electron on a catenoid surface. The catenoid is understood as a realization of a bridge connecting two graphene layer by a smooth surface. The curvature induces a symmetrical reflectionless potential well around the bridge with one bound-state for $m=0$. For $m\neq 0$, a centrifugal potential barrier arises controlling the tunnelling between the layers. An external electric field breaks the parity symmetry and provides a barrier that controls the conductance from one layer to another. By applying a constant magnetic field the effective potential exhibits a confining double-well potential nearby the bridge. We obtain the corresponding bound states and study the effects of the curvature on the Landau levels., Comment: 7 figures

Most studies on inequality in infant and child mortality compare average mortality rates between large groups of births, for example, comparing births from different countries, income groups, ethnicities, or different times. These studies do not measure within-group disparities. The few studies that have measured within-group variability in infant and child mortality have used tools from the income inequality literature, such as Gini indices. We show that the latter are inappropriate for infant and child mortality. We develop novel tools that are appropriate for analyzing infant and child mortality inequality, including inequality measures, covariate adjustments, and ANOVA methods. We illustrate how to handle uncertainty about complex inference targets, including ensembles of probabilities and kernel density estimates. We illustrate our methodology using a large data set from India, where we estimate infant and child mortality risk for over 400,000 births using a Bayesian hierarchical model. We show that most of the variance in mortality risk exists within groups of births, not between them, and thus that within-group mortality needs to be taken into account when assessing inequality in infant and child mortality. Our approach has broad applicability to many health indicators.

We prove a $p$-nilpotency criterion for finite groups in terms of the element orders of its $p'$-reduced sections that extends a nilpotency criterion by T{\u{a}}rn{\u{a}}uceanu.

For electrons above a superfluid helium film suspended on a specially designed dielectric substrate, $z=h(y)$, we obtain that both the transverse, along $z$, and the lateral, along $y$, quantizations are strongly enhanced due to a strong mutual coupling. The self-consistent quantum wires (QWs) with non-degenerated one-dimensional electron systems (1DESs) are obtained over a superfluid liquid helium (LH) suspended self-consistently on different dielectric substrates with a nanoscale modulation. A gap $\gtrsim 10$meV ($\gtrsim 1$meV) is obtained between the lowest two electron levels due to mainly the transverse (lateral) quantization. Our analytical model takes into account a strong interplay between the transverse and the lateral quantizations of an electron. It uses that the characteristic length (energy) along the former direction is essentially smaller (larger) than the one along the latter, in a close analogy with the adiabatic approximation., Comment: 10 pages, 11 figures

We provide a nilpotency criterion for fusion systems in terms of the vanishing of its cohomology with twisted coefficients.

These are lecture notes for a short course about spectral sequences that was held at M\'alaga, October 18--20 (2016), during the "Fifth Young Spanish Topologists Meeting". The approach was to illustrate the basic notions via fully computed examples arising from Algebraic Topology and Group Theory., Comment: 31 pages

Let $p$ be a prime number, let $d$ be an integer and let $G$ be a $d$-generated finite $p$-group of nilpotency class smaller than $p$. Then the number of possible isomorphism types for the mod $p$ cohomology algebra $H^*(G;{\mathbb F}_p)$ is bounded in terms of $p$ and $d$., Comment: 12 pages

We give a new proof of Quillen's conjecture for solvable groups via a geometric and explicit method. For p-solvable groups, we provide both a new proof using the Classification of Finite Simple Groups and an asymptotic version without employing it.

We prove the non-twisted case of Carlson's conjecture for any prime and we show how to proceed in the twisted case.

We describe the cohomology ring $H^*(J_2;\mathbb{F}_3)$ both as subring of $H^*(3^{1+2}_+;\mathbb{F}_3)$ and with an abstract presentation. We also give its Poincar\'{e} series. We use as tool a spectral sequence for the strongly closed $3$-subgroup of $J_2$. This method might be used to compute the cohomology of any finite simple group with a strongly closed $p$-subgroup.

We propose some conditions on a poset that produce a small chain complex for its homology. This allows to compare simplicial complexes and Quillen's complexes under the same prism. It turns out they differ in the existence or not of free faces in an acyclic complex.

We build a spectral sequence converging to the cohomology of a fusion system with a strongly closed subgroup. This spectral sequence is related to the Lyndon-Hochschild-Serre spectral sequence and coincides with it for the case of an extension of groups. Nevertheless, the new spectral sequence applies to more general situations like finite simple groups with a strongly closed subgroup and exotic fusion systems with a strongly closed subgroup. We prove an analogue of a result of Stallings in the context of fusion preserving homomorphisms and deduce Tate's p-nilpotency criterion as a corollary., Comment: 22 pages