Lower Bounds on the van der Waerden Numbers: Randomized- and Deterministic-Constructive

The van der Waerden number W(k,2) is the smallest integer n such that every 2-coloring of 1 to n has a monochromatic arithmetic progression of length k. The existence of such an n for any k is due to van der Waerden but known upper bounds on W(k,2) are enormous. Much effort was put into developing lower bounds on W(k,2). Most of these lower bound proofs employ the probabilistic method often in combination with the Lov\'asz Local Lemma. While these proofs show the existence of a 2-coloring that has no monochromatic arithmetic progression of length k they provide no efficient algorithm to find such a coloring. These kind of proofs are often informally called nonconstructive in contrast to constructive proofs that provide an efficient algorithm. This paper clarifies these notions and gives definitions for deterministic- and randomized-constructive proofs as different types of constructive proofs. We then survey the literature on lower bounds on W(k,2) in this light. We show how known nonconstructive lower bound proofs based on the Lov\'asz Local Lemma can be made randomized-constructive using the recent algorithms of Moser and Tardos. We also use a derandomization of Chandrasekaran, Goyal and Haeupler to transform these proofs into deterministic-constructive proofs. We provide greatly simplified and fully self-contained proofs and descriptions for these algorithms

Political Ambition and Legislative Behavior in the European Parliament

Members of the European Parliament (MEP) typically follow one of two career paths, either advancing within the European Parliament itself or returning to higher office in their home states. We argue that these different ambitions condition legislative behavior. Specifically, MEPs seeking domestic careers defect from group-leadership votes more frequently and oppose legislation that expands the purview of supranational institutions. We show how individual, domestic-party, and national level variables shape the careers available to MEPs and, in turn, their voting choices. To test the argument, we analyze MEPs' roll-call voting behavior in the 5th session of the EP (1999-2004) using a random effects model that captures idiosyncrasies in voting behavior across both individual MEPs and specific roll-call votes.published or submitted for publicationnot peer reviewe

Optical and Etching Studies of Native Aluminum Oxide Layers for Use in Microcavity Photonic Devices

Optical communication and computing systems are required to meet future information transfer and processing needs. Microcavity devices serve as an enabling technology to implement and integrate optoelectronic systems. It is important to understand the optical and mechanical properties of materials utilize within microcavity devices. Only then is it possible to accurately model and analyze structures. Microcavity structures incorporating a high aluminum content AlGaAs layers are designed, grown, processed, and measured. The processing of these devices includes the conversion of high aluminum-content AlGaAs layers to native aluminum oxide (AlO) layers through the process of thermal oxidation. This selective conversion of microcavity layers provides for the necessary electrical and optical confinement required to produce a plethora of microphotonic devices. The optical properties of hydrolyzed AlO layers within a monolithic microcavity structure are experimentally determined. Also examined is the induced AlO layer stress, a result of volumetric shrinkage. Additional mechanical properties of GaAs/AlAs multilayer Fabry-Perot etalon structures are explored through the process of chemical etching. A suitable chemical solution to selectively etch converted AlO layers within a microcavity structure is developed. This research provides the foundation for future III-V MEMS technology development

Lower Bounds on van der Waerden Numbers: Randomized- and Deterministic-Constructive

The van der Waerden number W(k,2) is the smallest integer n such that every 2-coloring of 1 to n has a monochromatic arithmetic progression of length k. The existence of such an n for any k is due to van der Waerden but known upper bounds on W(k,2) are enormous. Much effort was put into developing lower bounds on W(k,2). Most of these lower bound proofs employ the probabilistic method often in combination with the Lovasz Local Lemma. While these proofs show the existence of a 2-coloring that has no monochromatic arithmetic progression of length k they provide no efficient algorithm to find such a coloring. These kind of proofs are often informally called nonconstructive in contrast to constructive proofs that provide an efficient algorithm. This paper clarifies these notions and gives definitions for deterministic- and randomized-constructive proofs as different types of constructive proofs. We then survey the literature on lower bounds on W(k,2) in this light. We show how known nonconstructive lower bound proofs based on the Lovasz Local Lemma can be made randomized-constructive using the recent algorithms of Moser and Tardos. We also use a derandomization of Chandrasekaran, Goyal and Haeupler to transform these proofs into deterministic-constructive proofs. We provide greatly simplified and fully self-contained proofs and descriptions for these algorithms

A study on vortex flow control on inlet distortion in the re-engined 727-100 center inlet duct using computational fluid dynamics

Computational fluid dynamics was used to investigate the management of inlet distortion by the introduction of discrete vorticity sources at selected locations in the inlet for the purpose of controlling secondary flow. These sources of vorticity were introduced by means of vortex generators. A series of design observations were made concerning the importance of various vortex generator design parameters in minimizing engine face circumferential distortion. The study showed that vortex strength, generator scale, and secondary flow field structure have a complicated and interrelated influence on the engine face distortion, over and above the initial geometry and arrangement of the generators. The installed vortex generator performance was found to be a function of three categories of variables: the inflow conditions, the aerodynamic characteristics associated with the inlet duct, and the design parameters related to the geometry, arrangement, and placement of the vortex generators within the outlet duct itself

Exploring Simple, High Quality Out-of-Distribution Detection with L2 Normalization

We demonstrate that L2 normalization over feature space--an extremely simple method requiring no additional training strategies, hyperparameters, specialized loss functions or image augmentation--can produce competitive results for Out-of-Distribution (OoD) detection with a fraction of the training time (60 epochs with ResNet18, 100 epochs with ResNet50) required by more sophisticated methods. We show theoretically and empirically that our simple method decouples feature norms from the Neural Collapse (NC) constraints imposed by CE loss minimization. This decoupling preserves more feature-level information than a standard CE loss training regime, and allows greater separability between ID norms and near-OoD or far-OoD norms. Our goal is to provide insight toward fundamental, model-based approaches to OoD detection, with less reliance on external factors such as hyperparameter tuning or specialized training regimes. We suggest that L2 normalization provides a collection of benefits large enough to warrant consideration as a standard architecture choice

Comparison of continuous and discontinuous collisional bumpers: Dimensionally scaled impact experiments into single wire meshes

An experimental inquiry into the utility of discontinuous bumpers was conducted to investigate the collisional outcomes of impacts into single grid-like targets and to compare the results with more traditional bumper designs that employ continuous sheet stock. We performed some 35 experiments using 6.3 and 3.2 mm diameter spherical soda-lime glass projectiles at low velocities (less than 2.5 km/s) and 13 at velocities between 5 and 6 km/s, using 3.2 mm spheres only. The thrust of the experiments related to the characterization of collisional fragments as a function of target thickness or areal shield mass of both bumper designs. The primary product of these experiments was witness plates that record the resulting population of collisional fragments. Substantial interpretive and predictive insights into bumper performance were obtained. All qualitative observations (on the witness plates) and detailed measurements of displaced masses seem simply and consistently related only to bumper mass available for interaction with the impactor. This renders the grid bumper into the superior shield design. These findings present evidence that discontinuous bumpers are a viable concept for collisional shields, possibly superior to continuous geometries

WHICH DNA DAMAGE IS LIKELY TO BE RELEVANT IN HORMETIC RESPONSES?

Working under the assumption that hormesis is triggered by specific types of DNA damage, this report focuses on the types of damage which form the signature of ionizing radiation. The key attribute of the signature is the clustering of damage, arising from clusters of energy deposition such that more than one site within a 10 base pair segment of DNA has been chemically altered. A brief overview is given on what is currently believed to be the primary components of clustered damage produced by the direct effect. The overview draws primarily on studies that utilize electron paramagnetic resonance to measure free radical intermediates and gel electrophoresis to measure clustered damage in plasmid DNA. Based on this information, the threshold for a radiation induced biological response is calculated