Rigidity of convex polytopes under the dominant energy condition

Our work proves a rigidity theorem for initial data sets associated with convex polytopes, subject to the dominant energy condition. The theorem is established by utilizing an approach that involves approximating the polytope of interest with smooth convex domains and solving a boundary value problem for Dirac operators on these domains.Comment: All comments welcome! arXiv admin note: text overlap with arXiv:2301.0508

A note on dyadic approximation in Cantor's set

We consider the convergence theory for dyadic approximation in the middle-third Cantor set, $K$, for approximation functions of the form $\psi_{\tau}(n) = n^{-\tau}$ ($\tau \ge 0$). In particular, we show that for values of $\tau$ beyond a certain threshold we have that almost no point in $K$ is dyadically $\psi_{\tau}$-well approximable with respect to the natural probability measure on $K$. This refines a previous result in this direction obtained by the first, third, and fourth named authors (arXiv, 2020)

Period-colour and amplitude-colour relations in classical Cepheid variables IV: The multi-phase relations

The superb phase resolution and quality of the OGLE data on LMC and SMC Cepheids, together with existing data on Galactic Cepheids, are combined to study the period-colour (PC) and amplitude-colour (AC) relations as a function of pulsation phase. Our results confirm earlier work that the LMC PC relation (at mean light) is more consistent with two lines of differing slopes, separated at a period of 10 days. However, our multi-phase PC relations reveal much new structure which can potentially increase our understanding of Cepheid variables. These multi-phase PC relations provide insight into why the Galactic PC relation is linear but the LMC PC relation is non-linear. This is because the LMC PC relation is shallower for short (log P < 1) and steeper for long (log P > 1) period Cepheids than the corresponding Galactic PC relation. Both of the short and long period Cepheids in all three galaxies exhibit the steepest and shallowest slopes at phases around 0.75-0.85, respectively. A consequence is that the PC relation at phase ~0.8 is highly non-linear. Further, the Galactic and LMC Cepheids with log P > 1 display a flat slope in the PC plane at phases close to the maximum light. When the LMC period-luminosity (PL) relation is studied as a function of phase, we confirm that it changes with the PC relation. The LMC PL relation in V- and I-band near the phase of 0.8 provides compelling evidence that this relation is also consistent with two lines of differing slopes joined at a period close to 10 days.Comment: 12 pages, 1 table and 13 figures, MNRAS accepte

Adaptive forecasting in the presence of recent and ongoing structural change

We consider time series forecasting in the presence of ongoing structural change where both the time series dependence and the nature of the structural change are unknown. Methods that downweight older data, such as rolling regressions, forecast averaging over different windows and exponentially weighted moving averages, known to be robust to historical structural change, are found to be also useful in the presence of ongoing structural change in the forecast period. A crucial issue is how to select the degree of downweighting, usually defined by an arbitrary tuning parameter. We make this choice data dependent by minimizing forecast mean square error, and provide a detailed theoretical analysis of our proposal. Monte Carlo results illustrate the methods. We examine their performance on 191 UK and US macro series. Forecasts using data-based tuning of the data discount rate are shown to perform well

Liquid-infiltrated photonic crystals: Ohmic dissipation and broadening of modes

The pronounced light-matter interactions in photonic crystals make them interesting as opto-fludic "building blocks" for lab-on-a-chip applications. We show how conducting electrolytes cause dissipation and smearing of the density-of-states, thus altering decay dynamics of excited bio-molecules dissolved in the electrolyte. Likewise, we find spatial damping of propagating modes, of the order dB/cm, for naturally occurring electrolytes such as drinking water or physiological salt water.Comment: 9 pages including 2 figure

Autonomous Byte Stream Randomizer

Net-centric networking environments are often faced with limited resources and must utilize bandwidth as efficiently as possible. In networking environments that span wide areas, the data transmission has to be efficient without any redundant or exuberant metadata. The Autonomous Byte Stream Randomizer software provides an extra level of security on top of existing data encryption methods. Randomizing the data s byte stream adds an extra layer to existing data protection methods, thus making it harder for an attacker to decrypt protected data. Based on a generated crypto-graphically secure random seed, a random sequence of numbers is used to intelligently and efficiently swap the organization of bytes in data using the unbiased and memory-efficient in-place Fisher-Yates shuffle method. Swapping bytes and reorganizing the crucial structure of the byte data renders the data file unreadable and leaves the data in a deconstructed state. This deconstruction adds an extra level of security requiring the byte stream to be reconstructed with the random seed in order to be readable. Once the data byte stream has been randomized, the software enables the data to be distributed to N nodes in an environment. Each piece of the data in randomized and distributed form is a separate entity unreadable on its own right, but when combined with all N pieces, is able to be reconstructed back to one. Reconstruction requires possession of the key used for randomizing the bytes, leading to the generation of the same cryptographically secure random sequence of numbers used to randomize the data. This software is a cornerstone capability possessing the ability to generate the same cryptographically secure sequence on different machines and time intervals, thus allowing this software to be used more heavily in net-centric environments where data transfer bandwidth is limited

Autonomous Information Unit for Fine-Grain Data Access Control and Information Protection in a Net-Centric System

As communication and networking technologies advance, networks will become highly complex and heterogeneous, interconnecting different network domains. There is a need to provide user authentication and data protection in order to further facilitate critical mission operations, especially in the tactical and mission-critical net-centric networking environment. The Autonomous Information Unit (AIU) technology was designed to provide the fine-grain data access and user control in a net-centric system-testing environment to meet these objectives. The AIU is a fundamental capability designed to enable fine-grain data access and user control in the cross-domain networking environments, where an AIU is composed of the mission data, metadata, and policy. An AIU provides a mechanism to establish trust among deployed AIUs based on recombining shared secrets, authentication and verify users with a username, X.509 certificate, enclave information, and classification level. AIU achieves data protection through (1) splitting data into multiple information pieces using the Shamir's secret sharing algorithm, (2) encrypting each individual information piece using military-grade AES-256 encryption, and (3) randomizing the position of the encrypted data based on the unbiased and memory efficient in-place Fisher-Yates shuffle method. Therefore, it becomes virtually impossible for attackers to compromise data since attackers need to obtain all distributed information as well as the encryption key and the random seeds to properly arrange the data. In addition, since policy can be associated with data in the AIU, different user access and data control strategies can be included. The AIU technology can greatly enhance information assurance and security management in the bandwidth-limited and ad hoc net-centric environments. In addition, AIU technology can be applicable to general complex network domains and applications where distributed user authentication and data protection are necessary. AIU achieves fine-grain data access and user control, reducing the security risk significantly, simplifying the complexity of various security operations, and providing the high information assurance across different network domains

Brachial-Ankle Pulse Wave Velocity Is the Only Index of Arterial Stiffness That Correlates with a Mitral Valve Indices of Diastolic Dysfunction, but No Index Correlates with Left Atrial Size

The objective of this study was to determine the optimal assessment of arterial stiffness that relates to diastolic dysfunction. Forty-one patients had measurements of brachial-ankle pulse wave velocity (baPWV), carotid-femoral pulse wave velocity (cfPWV), ankle brachial index (ABI), pulse pressure (PP), and augmentation index (AIx). Diastolic dysfunction was evaluated by echocardiographic indices of the ratio of the peak early diastolic mitral valve velocity and the peak late diastolic velocity (E/A ratio), left atrial diameter, and left atrial volume indexes. There was a significant (P<0.05) correlation between baPWV and E/A ratio with an inverse relationship indicating that higher arterial stiffness was associated with greater diastolic dysfunction. In contrast, there was no significant correlation between E/A ratio and cfPWV, PP, ABI, or AIx. After multivariate analysis, the relationship between baPWV and E/A ratio remained significant (P<0.05), independent of age and systolic blood pressure (BP). There were no correlations between any index of vascular stiffness and left atrial dimension or volume. In summary, baPWV correlates with diastolic dysfunction, independent of a patient’s age and BP and is a better indicator of diastolic dysfunction than other indicators of arterial stiffness. baPWV has the utility of infering the presence of left ventricular diastolic dysfunction

Period-colour and amplitude-colour relations in classical Cepheid variables II: the Galactic Cepheid model

In this paper, we construct full amplitude non-linear hydrodynamical models of fundamental mode Galactic Cepheids and analyze the resulting theoretical period-colour and amplitude-colour relations at maximum, mean and minimum light. These theoretical relations match the general form of the observed relations well. This agreement is, to some extent, independent of the mass-luminosity relations used, pulsation code, numerical techniques, details of the input physics and methods to convert theoretical quantities, such as bolometric luminosity and temperature, to observational quantities, such as V band magnitudes or $(V-I)$ colours. We show that the period-colour and amplitude-colour properties of fundamental mode Galactic Cepheids with periods such that $\log (P)>0.8$ can be explained by a simple application of the Stefan-Boltzmann law and the interaction of the photosphere with the hydrogen ionization front. We discuss the implications of our results for explaining the behavior of Galactic Cepheid period-colour, and period-luminosity relations at mean light.Comment: 13 pages, 11 figures and 5 tables. MNRAS submitte