Some Combinatorial Properties of Hook Lengths, Contents, and Parts of Partitions

This paper proves a generalization of a conjecture of Guoniu Han, inspired originally by an identity of Nekrasov and Okounkov. The main result states that certain sums over partitions p of n, involving symmetric functions of the squares of the hook lengths of p, are polynomial functions of n. A similar result is obtained for symmetric functions of the contents and shifted parts of n.Comment: 20 pages. Correction of some inaccuracies, and a new Theorem 4.

Which regime works best in social welfare? Comparing outcomes of eight Dutch RCT experiments

Current technological innovations (automation, robotization, digitization, AI, big data) may have adverse employment effects notably for the low skilled welfare recipients. They face reduced chances for getting access to secure and fairly paid jobs also while two in three lack the basic qualifications needed to acquire the lowest level jobs, let alone that also more than one third consider themselves unfit to work due to serious physical or mental health issues. Therefore, eight Dutch municipalities (Deventer, Groningen, Nijmegen, Tilburg, Utrecht, Wageningen, Apeldoorn-Epe, Oss) started in the fall of 2017 and early 2018 a two-year long unique randomized control trial (RCT) to test three alternative regimes for people on welfare in which more than 5,000 recipients participated2. The treatments set up were (1) exemption/selfmanagement, that is exemption of the application obligations and rendering more trust and autonomy to the recipient for self-management, (2) intensive or tailored support, that is providing tailored and intensified counselling support to improve claimants’ work and social participation opportunities (e.g., in education, training or volunteer work) and (3) earnings release, that is rewarding welfare claimants for finding work by allowing participants to keep a larger part of their earnings on top of their benefit (work bonus). The experiments share some features of participation and basic income approaches even though their design and implementation are rather different. We found no evidence that the alternative welfare regimes have reduced employment effects compared to ‘workfare’ regimes. In some municipalities we find small positive significant effects on parttime and fulltime employment and on people’s self-efficacy, social trust and trust in caseworker’ support. No significant positive effects were found on health and wellbeing. The use of field experiments for testing the outcomes of alternative welfare regimes provides new avenues for welfare state policy in an era of rapid technological and economic change

Algorithms for Highly Symmetric Linear and Integer Programs

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of lower dimension. Combining this approach with knowledge of the geometry of feasible integer solutions yields an algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the number of constraints and quadratic in the dimension.Comment: 21 pages, 1 figure; some references and further comments added, title slightly change

Changes in the capacity of visual working memory in 5- to 10-year-olds

Using the Luck and Vogel change detection paradigm, we sought to investigate the capacity of visual working memory in 5-, 7-, and 10-year-olds. We found that performance on the task improved significantly with age and also obtained evidence that the capacity of visual working memory approximately doubles between 5 and 10 years of age, where it reaches adult levels of approximately three to four items

An investigation of VLF transmitter wave power in the inner radiation belt and slot region

Signals from man‐made Very Low Frequency (VLF) transmitters, used for communications with submarines, can leak into space and contribute to the dynamics of energetic electrons in the inner radiation belt and slot region. In this study we use ∼5 years of plasma wave data from the Van Allen Probe A satellite to construct new models of the observed wave power from VLF transmitters both as a function of L* and magnetic local time and geographic location. Average power peaks primarily on the nightside of the Earth for the VLF transmitters at low geographic latitudes. At higher latitudes the peak average power extends further in magnetic local time due to more extensive periods of nighttime in the winter months. Nighttime power is typically orders of magnitude more than that observed near noon, implying that loss rates from a given VLF transmitter will also maximize in this region. The observed power from any given VLF transmitter is tightly confined in longitude, with the nightside peak power typically falling by a factor of 10 within 10° longitude of the location of the peak signal. We show that the total average wave power from all VLF transmitters lies in the range 3–9 pT2 in the region 1.3<L*<3.0, with approximately 50% of this power emanating from three VLF transmitters, NWC, NAA, and DHO38

Twisting waves increase the visibility of nonlinear behaviour

Nonlinear behaviour for acoustic systems is readily measured at high acoustic pressures in gasses or bulk materials. However, at low acoustic pressures non-linear effects are not commonly observed. We find that by phase structuring acoustics beams, one observes evidence of non-linear behaviour at an acoustic pressure of 66.78 dB lower than non-structured beams in room temperature air. A bespoke 28-element ultrasonic phased array antenna was developed to generate short pulses that carry orbital angular momentum and are propagated over a short air channel. When sampling small areas of the wavefront, we observed a distinctive change in the frequency components near phase singularities. At these phase singularities the local propagation path is screwed, resulting in the collection signals from pulses traveling along different paths across the aperture of a microphone. The usually negligible frequency chirping that arises from nonlinear behaviour in air interfere at these singularity points and produce a distinctive distortion of the acoustic pulse. Simple physical movement in the system or super-sonic wave speeds do not yield similar results. Such distortions in measured frequency response near phase singularities could lead to errors for SONAR or acoustic communication systems, where received signals are integrated over a finite-area detector. With further development this behaviour could potentially lead to accurate measurement techniques for determining a material's nonlinear properties at lower acoustic pressure

Effects of VLF transmitter waves on the inner belt and slot region

Signals from very low frequency (VLF) transmitters can leak from the Earth‐ionosphere wave guide into the inner magnetosphere, where they propagate in the whistler mode and contribute to electron dynamics in the inner radiation belt and slot region. Observations show that the waves from each VLF transmitter are highly localized, peaking on the nightside in the vicinity of the transmitter. In this study we use ∼5 years of Van Allen Probes observations to construct global statistical models of the bounce‐averaged pitch angle diffusion coefficients for each individual VLF transmitter, as a function of L*, magnetic local time (MLT), and geographic longitude. We construct a 1‐D pitch angle diffusion model with implicit longitude and MLT dependence to show that VLF transmitter waves weakly scatter electrons into the drift loss cone. We find that global averages of the wave power, determined by averaging the wave power over MLT and longitude, capture the long‐term dynamics of the loss process, despite the highly localized nature of the waves in space. We use our new model to assess the role of VLF transmitter waves, hiss waves, and Coulomb collisions on electron loss in the inner radiation belt and slot region. At moderate relativistic energies, E∼500 keV, waves from VLF transmitters reduce electron lifetimes by an order of magnitude or more, down to the order of 200 days near the outer edge of the inner radiation belt. However, VLF transmitter waves are ineffective at removing multi–megaelectron volt electrons from either the inner radiation belt or slot region

Neonatal Multisensory Processing in Preterm and Term Infants Predicts Sensory Reactivity and Internalizing Tendencies in Early Childhood.

Multisensory processes include the capacity to combine information from the different senses, often improving stimulus representations and behavior. The extent to which multisensory processes are an innate capacity or instead require experience with environmental stimuli remains debated. We addressed this knowledge gap by studying multisensory processes in prematurely born and full-term infants. We recorded 128-channel event-related potentials (ERPs) from a cohort of 55 full-term and 61 preterm neonates (at an equivalent gestational age) in response to auditory, somatosensory, and combined auditory-somatosensory multisensory stimuli. Data were analyzed within an electrical neuroimaging framework, involving unsupervised topographic clustering of the ERP data. Multisensory processing in full-term infants was characterized by a simple linear summation of responses to auditory and somatosensory stimuli alone, which furthermore shared common ERP topographic features. We refer to the ERP topography observed in full-term infants as "typical infantile processing" (TIP). In stark contrast, preterm infants exhibited non-linear responses and topographies less-often characterized by TIP; there were distinct patterns of ERP topographies to multisensory and summed unisensory conditions. We further observed that the better TIP characterized an infant's ERPs, independently of prematurity, the more typical was the score on the Infant/Toddler Sensory Profile (ITSP) at 12 months of age and the less likely was the child to the show internalizing tendencies at 24 months of age. Collectively, these results highlight striking differences in the brain's responses to multisensory stimuli in children born prematurely; differences that relate to later sensory and internalizing functions

Mechanism, localization and cure of atrial arrhythmias occurring after a new intraoperative endocardial radiofrequency ablation procedure for atrial fibrillation

AbstractOBJECTIVESThe purpose of this study was to test a new pattern of radiofrequency ablation for atrial fibrillation (AFib) intended to optimize atrial activation, and to demonstrate the usefulness of catheter techniques for mapping and ablation of postoperative atrial arrhythmias.BACKGROUNDLinear radiofrequency lesions have been used to cure AFib, but the optimal pattern of lesions is unknown and postoperative tachyarrhythmias are common.METHODSA radial pattern of linear radiofrequency lesions (Star) was made using an endocardial open surgical approach in 25 patients. Postoperative arrhythmias were induced and characterized during electrophysiological studies in 15 patients.RESULTSThe AFib was abolished in most patients (91%), but atrial flutter (AFlut) occurred in 96% of patients postoperatively. At postoperative electrophysiological studies, 37 flutter morphologies were studied in 15 patients (46% spontaneous, cycle length [CL] 223 ± 25 ms). Seven mechanisms (lesions discontinuity, n = 6; focal mechanism, n = 1) of AFlut were characterized in six patients. In these cases, flutter was abolished using further catheter radiofrequency ablation. In the remaining cases, flutter was usually localized to an area involving the interatrial septum, but no critical isthmus was identified for ablation. After 16 ± 10 months, 15 patients (65%) were asymptomatic with (n = 3) or without (n = 12) antiarrhythmic medications. Eight (35%) patients had persistent arrhythmias. Postoperative atrial electrical activation was near physiological.CONCLUSIONSThe AFib may be abolished using a radial pattern of linear endocardial radiofrequency lesions, but postoperative AFlut is common even when lesions are made under optimal conditions. Endocardial mapping techniques can be used to characterize the flutter mechanisms, thus enabling subsequent successful catheter ablation

Three Coordination Frameworks with Copper Formate based Low Dimensional Motifs: Synthesis, Structure and Magnetic Properties

In this study we report the synthesis, crystal structures and magnetic properties of three frameworks wherein Cu cations are bridged by formate linkers into one-dimensional motifs. One of these compounds, Cu2(HCO2)3(C3N2H4)4(NO3), contains a ladder motif but remains paramagnetic to 2 K. This is likely because of the longer superexchange pathway along its chains due to the orientation of the Jahn-Teller axis of its Cu cations. In contrast Cu(HCO2)(NO3)(NH3)2 and Cu(HCO2)(ClO4)(NH3)2 feature Cu(HCO2) chains in which the Jahn-Teller axis is oriented perpendicular to the chain direction; these exhibit antiferromagnetic order below 12 and 7 K, respectively. Their magnetic susceptibilities are well fitted by a one-dimensional chain model but further examination of their magnetic properties reveals significant inter-chain magnetic coupling and a lack of spin dynamics. This suggests that these transitions correspond to the emergence of long-range magnetic order, highlighting the importance of detailed studies of frameworks containing low dimensional motifs to gain a deeper understanding of their magnetic behaviour