Conditional expectation and Bayes' rule for quantum random variables and positive operator valued measures

A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex Hilbert space, and a quantum random variable is a measurable operator valued function. Although quantum probability measures and random variables are used extensively in quantum mechanics, some of the fundamental probabilistic features of these structures remain to be determined. In this paper we take a step toward a better mathematical understanding of quantum random variables and quantum probability measures by introducing a quantum analogue for the expected value of a quantum random variable relative to a quantum probability measure. In so doing we are led to theorems for a change of quantum measure and a change of quantum variables. We also introduce a quantum conditional expectation which results in quantum versions of some standard identities for Radon-Nikodym derivatives. This allows us to formulate and prove a quantum analogue of Bayes' rule.Comment: v2: 16 pages, 0 figures; substantially revised and updated; shortened significantly with streamlined proofs and removal of several explicit calculation

Formally Verified Bundling and Appraisal of Evidence for Layered Attestations

Remote attestation is a technology for establishing trust in a remote computing system. Core to the integrity of the attestation mechanisms themselves are components that orchestrate, cryptographically bundle, and appraise measurements of the target system. Copland is a domain-specific language for specifying attestation protocols that operate in diverse, layered measurement topologies. In this work we formally define and verify the Copland Virtual Machine alongside a dual generalized appraisal procedure. Together these components provide a principled pipeline to execute and bundle arbitrary Copland-based attestations, then unbundle and evaluate the resulting evidence for measurement content and cryptographic integrity. All artifacts are implemented as monadic, functional programs in the Coq proof assistant and verified with respect to a Copland reference semantics that characterizes attestation-relevant event traces and cryptographic evidence structure. Appraisal soundness is positioned within a novel end-to-end workflow that leverages formal properties of the attestation components to discharge assumptions about honest Copland participants. These assumptions inform an existing model-finder tool that analyzes a Copland scenario in the context of an active adversary attempting to subvert attestation. An initial case study exercises this workflow through the iterative design and analysis of a Copland protocol and accompanying security architecture for an Unpiloted Air Vehicle demonstration platform. We conclude by instantiating a more diverse benchmark of attestation patterns called the "Flexible Mechanisms for Remote Attestation", leveraging Coq's built-in code synthesis to integrate the formal artifacts within an executable attestation environment

A Semantics for Attestation Protocols using Session Types in Coq

As our world becomes more connected, the average person must place more trust in cloud systems for everyday transactions. We rely on banks and credit card services to protect our money, hospitals to conceal and selectively disclose sensitive health information, and government agencies to protect our identity and uphold national security interests. However, establishing trust in remote systems is not a trivial task, especially in the diverse, distributed ecosystem of todays networked computers. Remote Attestation is a mechanism for establishing trust in a remotely running system where an Appraiser requests information from a target that can be used to evaluate its operational state. The target responds with evidence providing configuration information, run-time measurements, and authenticity meta-evidence used by the appraiser to determine if it trusts the target system. For Remote Attestation to be applied broadly, we must have Attestation Protocols that perform operations on a collection of applications, each of which must be measured differently. Verifying that these protocols behave as expected and accomplish their diverse attestation goals is a unique challenge. An important first step is to understand the structural properties and execution patterns they share. In this thesis I present a semantic framework for attestation protocol execution within the Coq verification environment including a protocol representation based on Session Types, a dependently typed model of perfect cryptography, and an operational execution semantics. The expressive power of dependent types constrains the structure of protocols and supports precise claims about their behavior. If we view attestation protocols as programming language expressions, we can borrow from standard language semantics techniques to model their execution. The proof framework ensures desirable properties of protocol execution that hold for all protocols. Within this framework, it is feasible to state and prove specialized properties such as authenticity and secrecy for individual protocols

Heterogeneity of Graphite Lithiation in State‐of‐the‐Art Cylinder‐Type Li‐Ion Cells

The two‐dimensional lithium distribution in the graphite anode was non‐destructively probed by spatially resolved neutron diffraction for a batch consisting of 34 different cylinder‐type (18650) Li‐ion batteries in fully charged state. The uniformity of the lithium distribution was quantified and correlated to the cell specifications/electrochemistry and to intrinsic cell parameters like electrode thickness, position of current collectors, etc. which were obtained by X‐ray micro‐computed tomography. Non‐uniformities in the lithiation state of the anode from a constant plateau have been observed for the majority of the studied cells. Their location corresponds to the positions of current tabs connecting the electrode stripes and areas of incomplete electrode coating at the beginning and the end of the electrode stripes. Four commonly used schemes of current lid connection were identified. Each of them displays its own effect on the uniformity of the lithiation at the anode and, therefore, variation of the intrinsic state‐of‐charge distribution and, most probably, the ageing behavior of the electrodes

Exploration of underutilized crop diversity of Capsicum peppers in their primary center of diversity in Bolivia and Peru

The genus Capsicum is a highly diverse complex of domesticated and wild species that displays abundant variation in its main center of domestication and diversity in Bolivia and Peru but that remains under-researched. New collecting expeditions undertaken in 2010 by the Instituto Nacional de Innovación Agraria (INIA) in Peru and the Centro de Investigaciones Fitoecogenéticas de Pairumani (CIFP) in Bolivia have significantly increased the size of the collections. INIA Peru now maintains 712 accessions of the five domesticated species, making it one of the largest and most diverse national collections of native Capsicum pepper varieties in the world. The collection in Bolivia contains 492 accessions, including the five domesticated species, four wild species, and one wild botanical variety of a domesticated species. We report on the identification of promising native Capsicum germplasm for potential use in the development of differentiated products. Identification of promising material representative of native Capsicum diversity in both collections followed several steps: (1) Identification of a core collection of nearly 100 accessions per country representing the different species and their geographic distribution. Dried samples of these accessions were biochemically screened for commercially interesting attributes including capsaicinoid content, polyphenols, antioxidant capacity, carotenoids, lipid content and color; (2) Based on results of the biochemical screening, sub-sets of 44 Bolivian and 39 Peruvian accessions were selected, representing the different species and variation in biochemical attributes; and (3) The selected materials were grown in different environments to identify the agro-ecological conditions were they best express the special properties of commercial interest. The biochemical screening and agromorphological characterization and evaluation revealed that Capsicum accessions from Bolivia and Peru have unique combinations of functional attributes, confirming that a wealth of commercially valuable properties can be found in Capsicum’s primary center of diversity. This study was financed by GIZ

Lithium distribution and transfer in high-power 18650-type Li-ion cells at multiple length scales

The distribution of lithium inside electrodes of a commercial Li-ion battery of 18650-type with LiFePO$_{4}$ cathode and graphite anode is investigated on different length scales using neutron diffraction, X-ray (synchrotron-based) diffraction and X-ray computed tomography. Evolution of 2D (in-plane) lithium distribution in lithiated graphite is monitored during charge/discharge using millimeter-sized spatial resolution. Micrometer-sized details of cell organization and lithiation of both the positive and negative electrodes are obtained from diffraction-based tomography applying synchrotron radiation. In-situ lithiation of the cathode over its thickness and development of the lithium concentration front during cell charge/discharge is traced by diffraction-based profiling with a micrometer-sized synchrotron beam in a single-layer electrochemical cell

2020 Kansas State University Industrial Hemp Dual-Purpose and Fiber Trial

Hemp is a broad term used to describe the many varieties of Cannabis sativa L. that produce less than 0.3% tetrahydrocannabinol (THC). The crop is globally significant, but only recently was allowed to be grown again in the United States. There are many uses for industrial hemp, which include oil, seed, and fiber, and the market for industrial hemp is rapidly growing as more states are legalizing its production. The market for industrial hemp is expected to grow from $5.33 billion in 2020 to 15.26 billion (15.8%) by 2027 as it gains more popularity (Grand View Research 2021, Valuates Reports 2021). The main components driving the industrial hemp market is the demand for CBD, which provides potential health benefits and hemp fiber. Biofuel from industrial hemp is also expected to stimulate the market and demand for hemp in the future. Varieties have been selected for improved fiber and grain production that have numerous industrial uses. However, the data only exist from a single growing season (2019) regarding adaptability or production of these varieties in Kansas (Griffin et al., 2020). Hemp could be added to diversify a crop rotation and to provide new market opportunities for growers